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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 | ||
| ||
Topological, differential and conformal geometry of surfaces / / Norbert A'Campo
| Topological, differential and conformal geometry of surfaces / / Norbert A'Campo |
| Autore | A'Campo N (Norbert) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (282 pages) |
| Disciplina | 516.36 |
| Collana | Universitext |
| Soggetto topico |
Geometry, Differential
Algebraic topology Geometry, Algebraic Superfícies de Riemann Geometria de Riemann |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-89032-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Chapter 1 Basic Differential Geometry -- 1.1 Fields on Open Sets in Real Vector Spaces -- 1.2 Closed Forms are Locally Exact -- 1.3 Fixed Point Theorems -- 1.4 The Abstract Field C Versus the R-Algebra C of Complex Numbers -- 1.5 Coordinates and Locally Smooth Rigidity Theorems -- 1.6 Differentiation in Banach Spaces -- 1.7 Sard's Theorem -- 1.8 The Morse Lemma and Morse Functions -- Chapter 2 The Geometry of Manifolds -- 2.1 Differentiable Manifolds -- 2.2 Fields on Manifolds -- 2.3 Frobenius' Integrability Condition -- 2.4 Foliations on Manifolds -- 2.5 The Topology of Connected, Compact Surfaces -- 2.6 Thoughts -- Chapter 3 Hyperbolic Geometry -- 3.1 The Hyperbolic Plane H = HI -- 3.2 Intermezzo: Higher Cross-Ratios -- 3.3 Hyperbolic Trigonometry -- 3.4 Hyperbolic Area -- 3.5 A Compact Hyperbolic Surface of Genus g ≥ 2 -- 3.6 The Riemann Sphere C U {∞} -- Chapter 4 Some Examples and Sources of Geometry -- 4.1 The Space of Norms -- 4.2 Combinatorial Geometry -- 4.3 Spaces of Involutions -- 4.4 Conflicts and Dynamics -- Chapter 5 Differential Topology of Surfaces -- 5.1 0- and 1-de Rham Cohomology of Surfaces -- 5.2 The Hyperbolic Plane Again, Now H = HJ -- 5.3 Reminder: Multi-Linear Algebra -- 5.4 Reminder: Holomorphic Functions in One Complex Variable -- 5.5 J-Laplace Operator and Metric -- 5.6 J-Surfaces -- Chapter 6 Riemann Surfaces -- 6.1 Riemann Surfaces as z- and as J-Surfaces -- 6.2 Natural Structures on the Space J(TS) -- 6.3 J-Fields and Integrability in Higher Dimensions -- 6.4 Integrability of Fibred J-Fields -- 6.5 Analysis of Laplace Operators on J-Surfaces -- 6.6 Topology of the Two-Point Green Function -- Chapter 7 Surfaces of Genus g = 0 -- 7.1 The Uniformization Theorem, the Genus g = 0 Case -- 7.2 Strong J-Rigidity -- 7.3 Strong J-Rigidity and Volume Stretching.
Chapter 8 Surfaces with Riemannian Metric -- 8.1 Riemannian Curvature -- 8.2 Topology of Surfaces and Curvature -- 8.3 Hyperbolic Length and Extremal Length -- Chapter 9 Outline: Uniformization by Spectral Determinant -- 9.1 A Theorem of Mueller-Wendland and Osgood-Phillips-Sarnak -- 9.2 Uniformization by Spectral Determinant, g ≥ 0 -- 9.3 Polyakov's String Dynamics -- Chapter 10 Uniformization by Energy -- 10.1 Energy and Curvature -- 10.2 The Uniformization Theorem, Case g ≥ 1, By Energy -- 10.3 The Uniformization Theorem, Case g = 1 -- 10.4 Comments About Uniformization, g = 0,1 or g ≥ 2 -- 10.5 Consequences of the Uniformization Theorem for Surfaces of Genus ≥1 -- 10.6 The ''Turn'' M(S) J(TS) -- Chapter 11 Families of Spaces -- 11.1 What Do Locally Trivial, Trivial and Constant Mean? -- 11.2 The Legendre Family -- Chapter 12 Functions on Riemann Surfaces -- 12.1 Meromorphic Functions on Riemann Surfaces -- 12.2 J-Harmonic 1-Differential Forms on J-Surfaces -- 12.3 Riemann's Theorem About the Sub-Space Holo(S,J) of Closed Forms Ω1,0 J (S,C) -- 12.4 Explicit Basis of Hol(S,J) for the Hyperelliptic Surface Defined By y2 = -x2g+1 + 1 -- 12.5 Why Functions? -- 12.6 The Field K(S) of Meromorphic Functions -- 12.7 Reconstruction of the Riemann Surface S From K(S) and its Subfield K0(S) -- Chapter 13 Line Bundles and Cohomology -- 13.1 Divisors and Line Bundles -- 13.2 Cech and Dolbeault Cohomology -- 13.3 Computations of Cohomology -- 13.4 More General Computation of Cohomology -- 13.5 Roch's Inequality -- 13.6 Line Bundles, Degree and Exact Cech Cohomology Sequences -- 13.7 Intermezzo: Global Infinitesimal Deformations of Locally Rigid Structures -- 13.8 Hyperelliptic Curves -- Chapter 14 Moduli Spaces and Teichmüller Spaces -- 14.1 Teichmüller Spaces as Smooth Manifolds -- 14.2 The Space Jμ(TSg) as a Symplectic Product. 14.3 The Space J(TS) as a Product With Three Factors -- 14.4 The Geometry of Tangent Vectors to a Teichmüller Space -- Chapter 15 Dimensions of Spaces of Holomorphic Sections -- 15.1 The Riemann-Roch Theorem -- 15.2 Consequences of the Riemann-Roch Theorem -- 15.3 The Birth of Serre Duality -- Chapter 16 The Teichmüller Curve and its Universal Property -- Chapter 17 Riemann Surfaces and Algebraic Curves -- 17.1 Chow's Theorem -- 17.2 Riemann Surfaces as Projective Curves -- Chapter 18 The Jacobian of a Riemann Surface -- 18.1 Vector Spaces Attached to a Riemann Surface -- 18.2 The Period Matrix and Riemann's Bilinear Relations -- 18.3 The Jacobian Jac(S) -- 18.4 The Abel-Jacobi Map -- Chapter 19 Special Metrics on J-Surfaces -- 19.1 The Bergman Metric -- 19.2 Special Metrics and Covering Spaces -- 19.3 The Energy of Canonical Embeddings -- Chapter 20 The Fundamental Group and Coverings -- 20.1 Simply Connected Riemann Surfaces and the Universal Uniformization Theorem -- 20.2 The Universal Cover and Uniformization of Riemann Surfaces -- Appendix A Reminder: Topology -- A.1 Topological Properties -- A.2 The Fundamental Group -- A.3 Covering Spaces -- A.4 Tessellations and Coverings -- References -- Index. |
| Record Nr. | UNINA-9910506397603321 |
|
A'Campo N (Norbert)
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Topological, differential and conformal geometry of surfaces / / Norbert A'Campo
| Topological, differential and conformal geometry of surfaces / / Norbert A'Campo |
| Autore | A'Campo N (Norbert) |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (282 pages) |
| Disciplina | 516.36 |
| Collana | Universitext |
| Soggetto topico |
Geometry, Differential
Algebraic topology Geometry, Algebraic Superfícies de Riemann Geometria de Riemann |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-89032-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Chapter 1 Basic Differential Geometry -- 1.1 Fields on Open Sets in Real Vector Spaces -- 1.2 Closed Forms are Locally Exact -- 1.3 Fixed Point Theorems -- 1.4 The Abstract Field C Versus the R-Algebra C of Complex Numbers -- 1.5 Coordinates and Locally Smooth Rigidity Theorems -- 1.6 Differentiation in Banach Spaces -- 1.7 Sard's Theorem -- 1.8 The Morse Lemma and Morse Functions -- Chapter 2 The Geometry of Manifolds -- 2.1 Differentiable Manifolds -- 2.2 Fields on Manifolds -- 2.3 Frobenius' Integrability Condition -- 2.4 Foliations on Manifolds -- 2.5 The Topology of Connected, Compact Surfaces -- 2.6 Thoughts -- Chapter 3 Hyperbolic Geometry -- 3.1 The Hyperbolic Plane H = HI -- 3.2 Intermezzo: Higher Cross-Ratios -- 3.3 Hyperbolic Trigonometry -- 3.4 Hyperbolic Area -- 3.5 A Compact Hyperbolic Surface of Genus g ≥ 2 -- 3.6 The Riemann Sphere C U {∞} -- Chapter 4 Some Examples and Sources of Geometry -- 4.1 The Space of Norms -- 4.2 Combinatorial Geometry -- 4.3 Spaces of Involutions -- 4.4 Conflicts and Dynamics -- Chapter 5 Differential Topology of Surfaces -- 5.1 0- and 1-de Rham Cohomology of Surfaces -- 5.2 The Hyperbolic Plane Again, Now H = HJ -- 5.3 Reminder: Multi-Linear Algebra -- 5.4 Reminder: Holomorphic Functions in One Complex Variable -- 5.5 J-Laplace Operator and Metric -- 5.6 J-Surfaces -- Chapter 6 Riemann Surfaces -- 6.1 Riemann Surfaces as z- and as J-Surfaces -- 6.2 Natural Structures on the Space J(TS) -- 6.3 J-Fields and Integrability in Higher Dimensions -- 6.4 Integrability of Fibred J-Fields -- 6.5 Analysis of Laplace Operators on J-Surfaces -- 6.6 Topology of the Two-Point Green Function -- Chapter 7 Surfaces of Genus g = 0 -- 7.1 The Uniformization Theorem, the Genus g = 0 Case -- 7.2 Strong J-Rigidity -- 7.3 Strong J-Rigidity and Volume Stretching.
Chapter 8 Surfaces with Riemannian Metric -- 8.1 Riemannian Curvature -- 8.2 Topology of Surfaces and Curvature -- 8.3 Hyperbolic Length and Extremal Length -- Chapter 9 Outline: Uniformization by Spectral Determinant -- 9.1 A Theorem of Mueller-Wendland and Osgood-Phillips-Sarnak -- 9.2 Uniformization by Spectral Determinant, g ≥ 0 -- 9.3 Polyakov's String Dynamics -- Chapter 10 Uniformization by Energy -- 10.1 Energy and Curvature -- 10.2 The Uniformization Theorem, Case g ≥ 1, By Energy -- 10.3 The Uniformization Theorem, Case g = 1 -- 10.4 Comments About Uniformization, g = 0,1 or g ≥ 2 -- 10.5 Consequences of the Uniformization Theorem for Surfaces of Genus ≥1 -- 10.6 The ''Turn'' M(S) J(TS) -- Chapter 11 Families of Spaces -- 11.1 What Do Locally Trivial, Trivial and Constant Mean? -- 11.2 The Legendre Family -- Chapter 12 Functions on Riemann Surfaces -- 12.1 Meromorphic Functions on Riemann Surfaces -- 12.2 J-Harmonic 1-Differential Forms on J-Surfaces -- 12.3 Riemann's Theorem About the Sub-Space Holo(S,J) of Closed Forms Ω1,0 J (S,C) -- 12.4 Explicit Basis of Hol(S,J) for the Hyperelliptic Surface Defined By y2 = -x2g+1 + 1 -- 12.5 Why Functions? -- 12.6 The Field K(S) of Meromorphic Functions -- 12.7 Reconstruction of the Riemann Surface S From K(S) and its Subfield K0(S) -- Chapter 13 Line Bundles and Cohomology -- 13.1 Divisors and Line Bundles -- 13.2 Cech and Dolbeault Cohomology -- 13.3 Computations of Cohomology -- 13.4 More General Computation of Cohomology -- 13.5 Roch's Inequality -- 13.6 Line Bundles, Degree and Exact Cech Cohomology Sequences -- 13.7 Intermezzo: Global Infinitesimal Deformations of Locally Rigid Structures -- 13.8 Hyperelliptic Curves -- Chapter 14 Moduli Spaces and Teichmüller Spaces -- 14.1 Teichmüller Spaces as Smooth Manifolds -- 14.2 The Space Jμ(TSg) as a Symplectic Product. 14.3 The Space J(TS) as a Product With Three Factors -- 14.4 The Geometry of Tangent Vectors to a Teichmüller Space -- Chapter 15 Dimensions of Spaces of Holomorphic Sections -- 15.1 The Riemann-Roch Theorem -- 15.2 Consequences of the Riemann-Roch Theorem -- 15.3 The Birth of Serre Duality -- Chapter 16 The Teichmüller Curve and its Universal Property -- Chapter 17 Riemann Surfaces and Algebraic Curves -- 17.1 Chow's Theorem -- 17.2 Riemann Surfaces as Projective Curves -- Chapter 18 The Jacobian of a Riemann Surface -- 18.1 Vector Spaces Attached to a Riemann Surface -- 18.2 The Period Matrix and Riemann's Bilinear Relations -- 18.3 The Jacobian Jac(S) -- 18.4 The Abel-Jacobi Map -- Chapter 19 Special Metrics on J-Surfaces -- 19.1 The Bergman Metric -- 19.2 Special Metrics and Covering Spaces -- 19.3 The Energy of Canonical Embeddings -- Chapter 20 The Fundamental Group and Coverings -- 20.1 Simply Connected Riemann Surfaces and the Universal Uniformization Theorem -- 20.2 The Universal Cover and Uniformization of Riemann Surfaces -- Appendix A Reminder: Topology -- A.1 Topological Properties -- A.2 The Fundamental Group -- A.3 Covering Spaces -- A.4 Tessellations and Coverings -- References -- Index. |
| Record Nr. | UNISA-996466390203316 |
|
A'Campo N (Norbert)
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
