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Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics
| Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics |
| Autore | Wootton Aaron |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (366 pages) |
| Disciplina | 515/.93 |
| Altri autori (Persone) |
BroughtonS. Allen
PaulhusJennifer |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Riemann surfaces
Automorphisms Group theory Functions of a complex variable -- Riemann surfaces Algebraic geometry -- Curves in algebraic geometry Group theory and generalizations -- Other groups of matrices -- Fuchsian groups and their generalizations (group-theoretic aspects) Group theory and generalizations -- Permutation groups -- Finite automorphism groups of algebraic, geometric, or combinatorial structures Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Arithmetic aspects of dessins d'enfants, Belyĭ theory Manifolds and cell complexes -- Low-dimensional topology in specific dimensions -- 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) |
| ISBN |
9781470467760
1470467763 |
| Classificazione | 30Fxx14Hxx20H1020B2511G3257K20 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Contents -- Preface -- The engaging symmetry of Riemann surfaces: A historical perspective -- 1. Introduction -- 2. Compact Riemann surfaces and their automorphisms -- 3. Hurwitz surfaces and groups and other interesting families -- 4. Maps and hypermaps -- 5. Dessins d'enfants and quasiplatonic surfaces -- 6. Connections with Galois theory -- References -- Future directions in automorphisms of surfaces, graphs, and other related topics -- 1. Introduction -- 2. Preliminaries -- 2.1. Conformal group actions on surfaces and their construction -- 2.1.1. Monodromy epimorphisms -- 2.1.2. Surface kernel epimorphisms -- 2.2. Equivalence of actions -- 3. Automorphism groups of Riemann surfaces -- 3.1. Classification results -- 3.2. Defining equations for surfaces and automorphisms -- 3.3. The genus spectrum of a group -- 3.4. Relationship with subgroups of mapping class groups -- 3.5. Full automorphism groups and maximal group orders -- 3.6. Signature realization -- 4. Families of Riemann surfaces and their moduli -- 4.1. Hurwitz spaces -- 4.2. Moduli and Teichmüller spaces -- 5. Curves -- 5.1. Extending results from hyperelliptic and superelliptic curves -- 5.2. Jacobian varieties -- 6. Graphs, dessins d'enfant and quasiplatonic surfaces -- 6.1. Dessins d'enfants -- 6.2. Quasiplatonic surfaces -- 6.3. Building surfaces and actions from a tiling -- 6.4. Further directions -- 7. Symmetries of surfaces -- 7.1. Symmetries of quasiplatonic surfaces -- 7.2. Existence of symmetries -- 7.3. Symmetric -gonal actions -- 8. Algorithms, computations, and explicit methods -- 8.1. Classifications -- 8.2. Equivalence relations -- 8.3. Problems on enumerating actions -- 9. Acknowledgments -- References -- Extending Harvey's surface kernel maps -- 1. Introduction -- 2. History and Methods -- 3. Notation -- 4. Harvey's results and Extensions.
5. Background: Summary of the Reidemeister-Schreier theory -- 6. Application of the Reidemeister-Schreier Theorem -- 7. The symmetric group ₃ and its multiplication table -- 8. Detailed Calculations for ₃ -- 9. Questions -- 10. Acknowledgments -- References -- A short proof of Greenberg's Theorem -- 1. Introduction -- 2. The proof -- 3. Remarks -- References -- Equivalence of finite group actions on Riemann surfaces and algebraic curves -- 1. Motivation and overview -- 2. Preliminaries -- 3. Rotation data of a -action -- 4. Equivalence of actions -- 5. Comparison of equivalence relations -- 6. Analysis of Conflation -- References -- Planar representations of group actions on surfaces -- 1. Introduction -- 2. Preliminaries -- 3. Skeletal uniqueness property -- 4. Skeletal signature spaces of SUP Groups: the strategy -- 5. The -SUP group case -- 6. The -SUP group case -- 7. The ²-SUP group case for odd -- 8. The 4-SUP group case -- Acknowledgments -- References -- Fiber product of Riemann surfaces -- 1. Introduction -- 2. The fiber product of Riemann surfaces -- 3. The strong field of moduli of the fiber product -- 4. Isogenous decomposition of the Jacobian variety of fiber products -- 5. Examples -- References -- One dimensional equisymmetric strata in moduli space -- 1. Introduction -- 2. Preliminaries -- 3. Covering -gonal strata by Hurwitz spaces -- 4. Case: Orbit genus 0 and 4 branch points -- References -- Arithmetic of dihedral origami -- 1. Introduction -- 2. Elliptic curve and origami set-up -- 3. Construction -- 4. Division polynomials -- 5. Galois representations -- 6. Diagram -- References -- Reduction of superelliptic Riemann surfaces -- 1. Introduction -- 2. Preliminaries -- 3. Reduction of the moduli point -- 4. Reduction of coefficients of binary forms -- 5. Concluding remarks -- References. Dessins d'enfants with a given bipartite graph -- 1. Introduction -- 2. Preliminaries -- 3. Proof of Theorem 1 -- 4. Some classical bipartite graphs -- Acknowledgment -- References -- On infinite octavalent polyhedral surfaces -- 1. Introduction -- 2. Background -- 3. 8(1,1,6) as Schwarz CLP minimal surface -- 4. A triangulated Swiss cross -- 5. Figure credits -- References -- Universal -gonal tessellations and their Petrie paths -- 1. Maps on surfaces -- 2. Algebraic maps -- 3. Universal maps and map subgroups -- 4. Hecke groups -- 5. Infinite periods -- 6. The universal -gonal map -- 7. Petrie paths -- 8. The special cases =4,6 -- 9. Even and odd vertices of Petrie paths -- 10. The principal Petrie paths of ℳ̂₅ -- References -- On the Riemann-Hurwitz formula for regular graph coverings -- 1. Introduction -- 2. Preliminary results and definitions -- 3. Groups acting on a graph without invertible edges -- 4. Groups acting on a graph with invertible edges -- Acknowledgments -- References -- Cyclic and dihedral actions on Klein surfaces with 2 boundary components -- 1. Introduction and preliminaries -- 2. The case odd -- 3. The case even: preliminary conditions -- 4. Cyclic groups -- 5. Dihedral groups -- 6. Concluding remarks -- References -- Finitely generated non-cocompact NEC groups -- 1. Introduction -- 2. Preliminaries -- 3. Surface symbols -- 4. Canonical presentation -- References -- Back Cover. |
| Record Nr. | UNINA-9910959086703321 |
Wootton Aaron
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Geometry at the Frontier : Symmetries and Moduli Spaces of Algebraic Varieties
| Geometry at the Frontier : Symmetries and Moduli Spaces of Algebraic Varieties |
| Autore | Comparin Paola |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (294 pages) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) |
EstevesEduardo
LangeHerbert |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Geometry, Algebraic
Curves, Algebraic Moduli theory Symmetry (Mathematics) Algebraic varieties Algebraic geometry -- Curves -- Riemann surfaces; Weierstrass points; gap sequences Functions of a complex variable -- Riemann surfaces Algebraic geometry -- Abelian varieties and schemes Algebraic geometry -- Abelian varieties and schemes -- Complex multiplication Algebraic geometry -- Curves -- Jacobians, Prym varieties Algebraic geometry -- Cycles and subschemes -- Transcendental methods, Hodge theory, Hodge conjecture Algebraic geometry -- Surfaces and higher-dimensional varieties -- Calabi-Yau manifolds Algebraic geometry -- Curves -- Automorphisms Algebraic geometry -- Surfaces and higher-dimensional varieties -- Automorphisms of surfaces and higher-dimensional varieties Algebraic geometry -- Algebraic groups -- Group actions on varieties or schemes (quotients) |
| ISBN |
9781470464226
1470464225 |
| Classificazione | 14H5530Fxx14Kxx14K2214H4014C3014J3214H3714J5014L30 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Contents -- Preface -- Lower and upper bounds for some generalized arcs -- Introduction -- 1. Basic definitions and background material -- 2. Some upper bounds for _{ }(2, ) -- 3. Some lower bounds for (2, ), ᵥ(2, ) and _{ }(2, ) -- Appendix: Magma programs -- Acknowledgments -- References -- Symmetries of order eight on K3 surfaces without high genus curves in the fixed locus -- Introduction -- 1. Basic facts -- 2. The fixed locus -- 3. The classification -- 4. Elliptic fibrations -- 5. Examples -- Acknowledgments -- References -- A decomposition of the Jacobian of a Humbert-Edge curve -- 1. Introduction -- 2. Main theorem -- 3. Proof of the main theorem -- 4. Geometric description of the decomposition of _{ } -- Acknowledgements -- References -- Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing -- Introduction -- 1. Preliminaries -- 2. Distortion of equivariant connections -- 3. Central extensions -- 4. Lifting gerbes and connective structures -- 5. Vanishing of Neeb's obstructions -- References -- Some algebraic and geometric properties of hyper-Kähler fourfold symmetries -- 1. Introduction -- 2. Prime order isometries of integral lattices -- 3. Order five symmetries of the Hilbert square of a K3 surface -- 4. Natural automorphisms of Kummer fourfolds -- Acknowledgments -- References -- On the existence of groups of automorphisms of compact Riemann and Klein surfaces -- 1. Introduction -- 2. Preliminaries -- 3. Finite groups as full automorphism groups -- 4. Surface normal subgroups of finite index -- 5. Necessary and sufficient conditions for the existence of a finite group action -- 6. Conditions for the existence of a finite full group action -- References -- Hyperbolic structures for Artin-Tits groups of spherical type -- 1. Introduction -- 2. Preliminaries.
3. Hyperbolic structures for ℬ_{ +1} -- 4. Generalizing to Artin-Tits groups of spherical type -- References -- Linear stability for line bundles over curves -- 1. Introduction -- 2. Extensions of line bundles -- 3. Linear stability and stability of Syzygy bundle -- References -- The contribution of W. L. Edge to the study of Humbert's curves -- 1. Introduction -- 2. Edge's approach to Humbert's curves -- 3. Chords and projections -- 4. Differentials and equations for ℋ -- 5. Planar representation of ᵢ -- 6. Moduli and degenerations -- References -- Deformations of noncompact Calabi-Yau manifolds, families and diamonds -- 1. Deformations of complex structures -- 2. Deformations of noncompact manifolds -- 3. Hyperkähler families -- 4. Adjoint orbits and cotangent bundles -- 5. Diamonds -- 6. Acknowledgments -- References -- A brute force computer aided proof of an existence result about extremal hyperbolic surfaces -- 1. Introduction -- 2. The main result -- 3. The brute force construction -- 4. Full details of the construction for the case =14. -- 5. End of the proof of Theorem 2.1 -- Acknowledgment -- References -- Complex surfaces with mutually non-biholomorphic universal covers -- 1. Introduction and statement of results -- 2. Preliminaries -- 3. Proof of the Theorem -- 4. Proof of the Proposition -- Acknowledgments -- References -- Hodge theory and moduli -- Outline -- References -- Constructing Jacobian varieties with many elliptic curves -- 1. Introduction -- 2. Some preliminaries -- 3. The constructions -- 4. Proof of Theorems 3 and 6 -- 5. Explicit examples -- Acknowledgments -- References -- Weil's Galois descent theorem from a computational point of view -- 1. Introduction -- 2. Preliminaries -- 3. Constructive proof of Weil's Galois descent theorem -- 4. Applications to complex algebraic varieties and field of moduli. 5. An Explicit Example: A curve of genus 5 -- References -- Subcovers of curves and moduli spaces -- 1. Introduction -- 2. Humbert surfaces -- 3. The geometry of Humbert surfaces -- 4. Connectedness properties -- 5. Intersections of Humbert surfaces -- 6. The refined Humbert invariant -- 7. Generalized Humbert schemes -- 8. Special quadratic forms -- 9. The components of ( ) -- 10. The structure of ( ) -- 11. Method of proof -- Acknowledgment -- References -- Algebraic geometry and convolutional codes -- 1. Introduction -- 2. Convolutional codes. Classification and free distance -- 3. Convolutional Goppa codes -- 4. Further applications and future work -- References -- Adelic and idelic pairings related to Weil reciprocity on algebraic curves -- 1. Introduction -- 2. Adeles, ideles, and the function field -- 3. Reciprocity pairing on ideles -- 4. The Main Quotient (Σ_{ }*)^{\pperp}/Σ_{ }* -Topology -- 5. The Main Quotient (Σ_{ }*)^{\pperp}/Σ_{ }* -Geometry -- 6. Applications -- Acknowledgments -- References -- Remarks on the size of the Tamagawa product -- 1. Tamagawa factors -- 2. Notation and preliminaries -- 3. Smallness of the Tamagawa factor -- 4. Diophantine consequences -- References -- Back Cover. |
| Altri titoli varianti | Geometry at the Frontier |
| Record Nr. | UNINA-9910962812303321 |
|
Comparin Paola
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| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Functions of a complex variable -- Riemann surfaces
(2)
- Algebraic geometry -- Abelian varieties and schemes (1)
- Algebraic geometry -- Abelian varieties and schemes -- Complex multiplication (1)
- Algebraic geometry -- Algebraic groups -- Group actions on varieties or schemes (quotients) (1)
- Algebraic geometry -- Curves -- Automorphisms (1)