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Algebraic Curves and Riemann Surfaces for Undergraduates [[electronic resource] ] : The Theory of the Donut / / by Anil Nerode, Noam Greenberg
| Algebraic Curves and Riemann Surfaces for Undergraduates [[electronic resource] ] : The Theory of the Donut / / by Anil Nerode, Noam Greenberg |
| Autore | Nerode Anil <1932-> |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (456 pages) |
| Disciplina | 515.93 |
| Soggetto topico |
Algebraic geometry
Functions of complex variables Global analysis (Mathematics) Manifolds (Mathematics) Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Corbes algebraiques Geometria algebraica Superfícies de Riemann |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-11616-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout’s theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions. |
| Record Nr. | UNISA-996508571503316 |
Nerode Anil <1932->
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Algebraic Curves and Riemann Surfaces for Undergraduates : The Theory of the Donut / / by Anil Nerode, Noam Greenberg
| Algebraic Curves and Riemann Surfaces for Undergraduates : The Theory of the Donut / / by Anil Nerode, Noam Greenberg |
| Autore | Nerode Anil <1932-> |
| Edizione | [1st ed. 2022.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
| Descrizione fisica | 1 online resource (456 pages) |
| Disciplina | 515.93 |
| Soggetto topico |
Geometry, Algebraic
Functions of complex variables Global analysis (Mathematics) Manifolds (Mathematics) Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Corbes algebraiques Geometria algebraica Superfícies de Riemann |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-11616-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout’s theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions. |
| Record Nr. | UNINA-9910644265203321 |
|
Nerode Anil <1932->
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Decomposition of Jacobians by Prym varieties / / Herbert Lange, Rubí E. Rodríguez
| Decomposition of Jacobians by Prym varieties / / Herbert Lange, Rubí E. Rodríguez |
| Autore | Lange H (Herbert), <1943-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (261 pages) |
| Disciplina | 905 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Curves, Algebraic
Corbes algebraiques Geometria algebraica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-10145-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Notations -- 1 Introduction -- 2 Preliminaries and Basic Results -- 2.1 Line Bundles on Abelian Varieties -- 2.2 Polarized Abelian Varieties -- 2.3 Endomorphisms of Abelian Varieties -- 2.4 The Weil Form on K(L) -- 2.5 Symmetric Idempotents -- 2.6 Abelian Subvarieties of a Polarized Abelian Variety -- 2.6.1 The Principally Polarized Case -- 2.6.2 The Case of an Arbitrary Polarization -- 2.7 Poincaré's Reducibility Theorem -- 2.8 Complex and Rational Representations of Finite Groups -- 2.9 The Isotypical and Group Algebra Decompositions -- 2.9.1 Generalities -- 2.9.2 Induced Action on the Tangent Space -- 2.10 Action of a Hecke Algebra on an Abelian Variety -- 3 Prym Varieties -- 3.1 Finite Covers of Curves -- 3.1.1 Definitions and Elementary Results -- 3.1.2 The Signature of a Galois Cover -- 3.1.3 The Geometric Signature of a Galois Cover -- 3.2 Prym Varieties of Covers of Curves -- 3.2.1 Definition of Prym Varieties -- 3.2.2 Polarizations of Prym Varieties -- 3.2.3 The Degrees of the Decomposition Isogeny -- 3.2.4 Degrees of Isogenies Arising from a Decomposition of f: C"0365C C -- 3.3 Two-Division Points of Prym Varieties of Double Covers -- 3.4 Prym Varieties of Pairs of Covers -- 3.5 Galois Covers of Curves -- 3.5.1 Jacobians and Pryms of Intermediate Covers -- 3.5.2 Isotypical and Group Algebra Decompositions of Intermediate Covers -- 3.5.3 Decomposition of the Tangent Space of the Prym Variety Associated to a Pair of Subgroups -- 3.5.4 The Dimension of an Isotypical Component -- 4 Covers of Degree 2 and 3 -- 4.1 Covers of Degree 2 -- 4.2 Covers of Degree 3 -- 4.2.1 Cyclic Covers of Degree 3 -- 4.2.2 Non-cyclic Covers of Degree 3: The Galois Closure -- 4.2.3 The Irreducible Rational Representations of S3 -- 4.2.4 Curves with an S3-action: Decomposition of J"0365J.
4.2.5 The Degree of the Isogeny ψ -- 5 Covers of Degree 4 -- 5.1 Cyclic Covers of Degree 4 -- 5.2 The Klein Group of Order 4 -- 5.2.1 Decompositions of J"0365J -- 5.2.2 Degrees of Some Isogenies -- 5.2.3 Proof of Proposition 5.2.5 -- 5.3 The Dihedral Group of Order 8 -- 5.3.1 Ramification and Genera -- 5.3.2 Decompositions of J"0365J -- 5.3.3 An Isogeny Coming from an Action of a Quotient Group -- 5.3.4 A Generalization of the Bigonal Construction -- 5.4 The Bigonal Construction -- 5.4.1 Definition and First Properties -- 5.4.2 Determination of the Bigonal Construction in the Non-Galois Case -- 5.4.3 The Bigonal Construction over C =P1 -- 5.4.4 Pantazis' Theorem -- 5.5 The Alternating Group of Degree 4 -- 5.5.1 Ramification and Genera -- 5.5.2 Decompositions of J -- 5.5.3 A Generalization of the Trigonal Construction -- 5.6 The Trigonal Construction for Covers with Group A4 -- 5.7 The Symmetric Group S4 -- 5.7.1 Ramification and Genera -- 5.7.2 Decomposition of J"0365J -- 5.7.3 Isogenies Arising from Actions of Subgroups of S4 -- 5.7.4 An Isogeny Arising from the Action of a Quotient of S4 -- 5.8 Another Generalization of the Trigonal Construction -- 5.8.1 Statement and Preparations -- 5.8.2 The Trigonal Construction -- 5.8.3 The Degree of γ in the General Principally Polarized Case -- 5.8.4 The Non-Principally Polarized Case -- 6 Some Series of Group Actions -- 6.1 Cyclic Covers -- 6.1.1 Notation and First Results -- 6.1.2 Cyclic Covers of Degree p -- 6.1.3 Cyclic Covers of Degree p2 -- 6.1.4 Cyclic Covers of Degree pq -- 6.2 Covers with Dihedral Group Action -- 6.2.1 The Irreducible Rational Representations of Dn -- 6.2.2 Curves with Dp-Action: Ramifications and Genera -- 6.2.3 Curves with Dp-Action: Decompositions of J"0365J -- 6.2.4 The Degree of the Isogeny φ -- 6.2.5 Curves with D2α-Action, α≥2. 6.2.6 Curves with a D2p-Action: Ramification and Genera -- 6.2.7 Curves with D2p-Action: Decomposition of J"0365J -- 6.2.8 Some Isogenies Between Prym Subvarieties -- 6.3 Semidirect Products of a Group of Order 3 by Powers of K4 -- 6.3.1 The Group Gn -- 6.3.2 The Diagram of Subcovers of a Curve with Gn-Action -- 6.3.3 A Jacobian Isogenous to the Product a Big Number of Jacobians -- 7 Some Special Groups and Complete Decomposability -- 7.1 The Alternating Group A5 -- 7.1.1 The Irreducible Rational Representations of A5 -- 7.1.2 Ramification and Genera -- 7.1.3 Decompositions of J"0365J -- 7.1.4 Some Isogenies Between Prym Varieties of Subcovers -- 7.2 Groups with Schur Index Larger Than One -- 7.2.1 The Group of Hamiltonian Quaternions -- 7.2.2 A Group of Order 24 -- 7.3 Completely Decomposable Jacobians -- 7.3.1 The Theorem of Ekedahl-Serre -- 7.3.2 Examples -- 7.3.3 Intermediate Covers -- Bibliography -- Index. |
| Record Nr. | UNINA-9910632490603321 |
|
Lange H (Herbert), <1943->
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Decomposition of Jacobians by Prym varieties / / Herbert Lange, Rubí E. Rodríguez
| Decomposition of Jacobians by Prym varieties / / Herbert Lange, Rubí E. Rodríguez |
| Autore | Lange H (Herbert), <1943-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (261 pages) |
| Disciplina | 905 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Curves, Algebraic
Corbes algebraiques Geometria algebraica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-10145-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Notations -- 1 Introduction -- 2 Preliminaries and Basic Results -- 2.1 Line Bundles on Abelian Varieties -- 2.2 Polarized Abelian Varieties -- 2.3 Endomorphisms of Abelian Varieties -- 2.4 The Weil Form on K(L) -- 2.5 Symmetric Idempotents -- 2.6 Abelian Subvarieties of a Polarized Abelian Variety -- 2.6.1 The Principally Polarized Case -- 2.6.2 The Case of an Arbitrary Polarization -- 2.7 Poincaré's Reducibility Theorem -- 2.8 Complex and Rational Representations of Finite Groups -- 2.9 The Isotypical and Group Algebra Decompositions -- 2.9.1 Generalities -- 2.9.2 Induced Action on the Tangent Space -- 2.10 Action of a Hecke Algebra on an Abelian Variety -- 3 Prym Varieties -- 3.1 Finite Covers of Curves -- 3.1.1 Definitions and Elementary Results -- 3.1.2 The Signature of a Galois Cover -- 3.1.3 The Geometric Signature of a Galois Cover -- 3.2 Prym Varieties of Covers of Curves -- 3.2.1 Definition of Prym Varieties -- 3.2.2 Polarizations of Prym Varieties -- 3.2.3 The Degrees of the Decomposition Isogeny -- 3.2.4 Degrees of Isogenies Arising from a Decomposition of f: C"0365C C -- 3.3 Two-Division Points of Prym Varieties of Double Covers -- 3.4 Prym Varieties of Pairs of Covers -- 3.5 Galois Covers of Curves -- 3.5.1 Jacobians and Pryms of Intermediate Covers -- 3.5.2 Isotypical and Group Algebra Decompositions of Intermediate Covers -- 3.5.3 Decomposition of the Tangent Space of the Prym Variety Associated to a Pair of Subgroups -- 3.5.4 The Dimension of an Isotypical Component -- 4 Covers of Degree 2 and 3 -- 4.1 Covers of Degree 2 -- 4.2 Covers of Degree 3 -- 4.2.1 Cyclic Covers of Degree 3 -- 4.2.2 Non-cyclic Covers of Degree 3: The Galois Closure -- 4.2.3 The Irreducible Rational Representations of S3 -- 4.2.4 Curves with an S3-action: Decomposition of J"0365J.
4.2.5 The Degree of the Isogeny ψ -- 5 Covers of Degree 4 -- 5.1 Cyclic Covers of Degree 4 -- 5.2 The Klein Group of Order 4 -- 5.2.1 Decompositions of J"0365J -- 5.2.2 Degrees of Some Isogenies -- 5.2.3 Proof of Proposition 5.2.5 -- 5.3 The Dihedral Group of Order 8 -- 5.3.1 Ramification and Genera -- 5.3.2 Decompositions of J"0365J -- 5.3.3 An Isogeny Coming from an Action of a Quotient Group -- 5.3.4 A Generalization of the Bigonal Construction -- 5.4 The Bigonal Construction -- 5.4.1 Definition and First Properties -- 5.4.2 Determination of the Bigonal Construction in the Non-Galois Case -- 5.4.3 The Bigonal Construction over C =P1 -- 5.4.4 Pantazis' Theorem -- 5.5 The Alternating Group of Degree 4 -- 5.5.1 Ramification and Genera -- 5.5.2 Decompositions of J -- 5.5.3 A Generalization of the Trigonal Construction -- 5.6 The Trigonal Construction for Covers with Group A4 -- 5.7 The Symmetric Group S4 -- 5.7.1 Ramification and Genera -- 5.7.2 Decomposition of J"0365J -- 5.7.3 Isogenies Arising from Actions of Subgroups of S4 -- 5.7.4 An Isogeny Arising from the Action of a Quotient of S4 -- 5.8 Another Generalization of the Trigonal Construction -- 5.8.1 Statement and Preparations -- 5.8.2 The Trigonal Construction -- 5.8.3 The Degree of γ in the General Principally Polarized Case -- 5.8.4 The Non-Principally Polarized Case -- 6 Some Series of Group Actions -- 6.1 Cyclic Covers -- 6.1.1 Notation and First Results -- 6.1.2 Cyclic Covers of Degree p -- 6.1.3 Cyclic Covers of Degree p2 -- 6.1.4 Cyclic Covers of Degree pq -- 6.2 Covers with Dihedral Group Action -- 6.2.1 The Irreducible Rational Representations of Dn -- 6.2.2 Curves with Dp-Action: Ramifications and Genera -- 6.2.3 Curves with Dp-Action: Decompositions of J"0365J -- 6.2.4 The Degree of the Isogeny φ -- 6.2.5 Curves with D2α-Action, α≥2. 6.2.6 Curves with a D2p-Action: Ramification and Genera -- 6.2.7 Curves with D2p-Action: Decomposition of J"0365J -- 6.2.8 Some Isogenies Between Prym Subvarieties -- 6.3 Semidirect Products of a Group of Order 3 by Powers of K4 -- 6.3.1 The Group Gn -- 6.3.2 The Diagram of Subcovers of a Curve with Gn-Action -- 6.3.3 A Jacobian Isogenous to the Product a Big Number of Jacobians -- 7 Some Special Groups and Complete Decomposability -- 7.1 The Alternating Group A5 -- 7.1.1 The Irreducible Rational Representations of A5 -- 7.1.2 Ramification and Genera -- 7.1.3 Decompositions of J"0365J -- 7.1.4 Some Isogenies Between Prym Varieties of Subcovers -- 7.2 Groups with Schur Index Larger Than One -- 7.2.1 The Group of Hamiltonian Quaternions -- 7.2.2 A Group of Order 24 -- 7.3 Completely Decomposable Jacobians -- 7.3.1 The Theorem of Ekedahl-Serre -- 7.3.2 Examples -- 7.3.3 Intermediate Covers -- Bibliography -- Index. |
| Record Nr. | UNISA-996499869003316 |
|
Lange H (Herbert), <1943->
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier
| Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier |
| Autore | Erlandsson Viveka |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (233 pages) |
| Disciplina | 516.352 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Curves, Algebraic
Curves, Algebraic - Data processing Corbes Corbes algebraiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08705-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- Notation -- 1 Introduction -- Some Things that the Reader Will Not Find in This Book -- What the Reader Will Find Here -- A Comment on the Way This Book Is Written -- 2 Read Me -- Curves, Multicurves, and Arcs -- Intersection Number -- Geodesic Representatives -- Random Geodesics. Or Length Versus Intersections -- Space of Geodesics -- Geodesics Projecting into a Fixed Compact Set -- Laminations -- Hausdorff Limits -- Mapping Class Group -- Shortening Curves -- 3 Geodesic Currents -- Definition and Examples -- Curves as Currents -- Weighted Multicurves -- Measured Laminations -- The Space of Geodesic Currents -- Interesting Subsets of C(Σ) -- Intersection Form -- Characterization of Measured Laminations -- Filling Currents -- The Mapping Class Group Action -- Mapping Class Group Action on the Set of Filling Currents -- Comments (The Liouville Current) -- 4 Train Tracks -- Train Tracks as Smoothly Embedded Complexes -- Almost Geodesic Train Tracks -- Band Complexes and Train Tracks -- Curves and Laminations Carried by Train Tracks -- Weights and Recurrence -- Switch Equations -- Thurston Measure -- First Counting Result -- Masur's Ergodicity Theorem -- An Example: The Case of the Once Punctured Torus -- Comments -- Piecewise Linear Structure -- Symplectic Structure -- Weil-Petersson Volume Form -- Other Interesting Measures on ML(S) -- 5 Radallas -- Terminology -- The Game of Cars -- Almost Geodesic Radallas -- Finding Almost Geodesic Radallas -- Generic Curves -- Comments: Expected Angle of Self-Intersection -- 6 Subconvergence of Measures -- Idea of the Proof of Theorem 6.1 -- Local Map -- Global Map -- New Measures -- Comments -- 7 Approximating the Thurston Measure -- Dribbling -- Radallas Carrying the Curves in Θσ0 -- Reducing to a Linear Algebra Problem -- Proof of Proposition 7.2.
Comments -- 8 The Main Theorem -- Notation and the Constants -- The Theorem -- The Fundamental Domain -- The Meat -- The Not Ker-Invariant Case -- Comments -- 9 Counting Curves -- Main Curve Counting Theorem -- Frequencies and Relative Frequencies -- Functions on the Space of Currents -- 10 Counting Square-Tiled Surfaces -- Square-Tiled Surfaces -- Recovering Square-Tiled Surface Structures from Multicurves -- Square-Tiled Surfaces of Given Type -- Counting -- Comments -- 11 Statistics of Simple Curves -- Credit to Kasra -- Hard Data -- A Formula for c(α0) for Simple Curves -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-Separating Curves in Closed Surfaces -- Combinatorial Computation -- Changing Weights -- Comments -- 12 Smörgåsbord -- Random Pants Decompositions -- Lattice Point Counting in Teichmüller Space -- Genericty of pseudo-Anosov Elements -- A Radon Measures -- Point-Set Topology -- Weak-*-Topology -- Sequential Compactness -- B Computing Thurston Volumes -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-separating Curves in Closed Surfaces -- References -- Index. |
| Record Nr. | UNISA-996490345903316 |
|
Erlandsson Viveka
|
||
| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier
| Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier |
| Autore | Erlandsson Viveka |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (233 pages) |
| Disciplina | 516.352 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Curves, Algebraic
Curves, Algebraic - Data processing Corbes Corbes algebraiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08705-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- Notation -- 1 Introduction -- Some Things that the Reader Will Not Find in This Book -- What the Reader Will Find Here -- A Comment on the Way This Book Is Written -- 2 Read Me -- Curves, Multicurves, and Arcs -- Intersection Number -- Geodesic Representatives -- Random Geodesics. Or Length Versus Intersections -- Space of Geodesics -- Geodesics Projecting into a Fixed Compact Set -- Laminations -- Hausdorff Limits -- Mapping Class Group -- Shortening Curves -- 3 Geodesic Currents -- Definition and Examples -- Curves as Currents -- Weighted Multicurves -- Measured Laminations -- The Space of Geodesic Currents -- Interesting Subsets of C(Σ) -- Intersection Form -- Characterization of Measured Laminations -- Filling Currents -- The Mapping Class Group Action -- Mapping Class Group Action on the Set of Filling Currents -- Comments (The Liouville Current) -- 4 Train Tracks -- Train Tracks as Smoothly Embedded Complexes -- Almost Geodesic Train Tracks -- Band Complexes and Train Tracks -- Curves and Laminations Carried by Train Tracks -- Weights and Recurrence -- Switch Equations -- Thurston Measure -- First Counting Result -- Masur's Ergodicity Theorem -- An Example: The Case of the Once Punctured Torus -- Comments -- Piecewise Linear Structure -- Symplectic Structure -- Weil-Petersson Volume Form -- Other Interesting Measures on ML(S) -- 5 Radallas -- Terminology -- The Game of Cars -- Almost Geodesic Radallas -- Finding Almost Geodesic Radallas -- Generic Curves -- Comments: Expected Angle of Self-Intersection -- 6 Subconvergence of Measures -- Idea of the Proof of Theorem 6.1 -- Local Map -- Global Map -- New Measures -- Comments -- 7 Approximating the Thurston Measure -- Dribbling -- Radallas Carrying the Curves in Θσ0 -- Reducing to a Linear Algebra Problem -- Proof of Proposition 7.2.
Comments -- 8 The Main Theorem -- Notation and the Constants -- The Theorem -- The Fundamental Domain -- The Meat -- The Not Ker-Invariant Case -- Comments -- 9 Counting Curves -- Main Curve Counting Theorem -- Frequencies and Relative Frequencies -- Functions on the Space of Currents -- 10 Counting Square-Tiled Surfaces -- Square-Tiled Surfaces -- Recovering Square-Tiled Surface Structures from Multicurves -- Square-Tiled Surfaces of Given Type -- Counting -- Comments -- 11 Statistics of Simple Curves -- Credit to Kasra -- Hard Data -- A Formula for c(α0) for Simple Curves -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-Separating Curves in Closed Surfaces -- Combinatorial Computation -- Changing Weights -- Comments -- 12 Smörgåsbord -- Random Pants Decompositions -- Lattice Point Counting in Teichmüller Space -- Genericty of pseudo-Anosov Elements -- A Radon Measures -- Point-Set Topology -- Weak-*-Topology -- Sequential Compactness -- B Computing Thurston Volumes -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-separating Curves in Closed Surfaces -- References -- Index. |
| Record Nr. | UNINA-9910595045203321 |
|
Erlandsson Viveka
|
||
| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topics surrounding the combinatorial anabelian geomtry of hyperbolic curves II : tripods and combinatorial cuspidalization / / Yuichiro Hoshi and Shinichi Mochizuki
| Topics surrounding the combinatorial anabelian geomtry of hyperbolic curves II : tripods and combinatorial cuspidalization / / Yuichiro Hoshi and Shinichi Mochizuki |
| Autore | Hoshi Yuichiro |
| Pubbl/distr/stampa | Gateway East, Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (174 pages) |
| Disciplina | 516.352 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Abelian categories
Curves, Algebraic Corbes algebraiques Categories abelianes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-1096-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996475750503316 |
|
Hoshi Yuichiro
|
||
| Gateway East, Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Topics surrounding the combinatorial anabelian geomtry of hyperbolic curves II : tripods and combinatorial cuspidalization / / Yuichiro Hoshi and Shinichi Mochizuki
| Topics surrounding the combinatorial anabelian geomtry of hyperbolic curves II : tripods and combinatorial cuspidalization / / Yuichiro Hoshi and Shinichi Mochizuki |
| Autore | Hoshi Yuichiro |
| Pubbl/distr/stampa | Gateway East, Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (174 pages) |
| Disciplina | 516.352 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Abelian categories
Curves, Algebraic Corbes algebraiques Categories abelianes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-1096-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910574084103321 |
|
Hoshi Yuichiro
|
||
| Gateway East, Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
