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Introduction to compact Riemann surfaces and dessins d'enfants / / Ernesto Girondo, Gabino González-Diez [[electronic resource]]
| Introduction to compact Riemann surfaces and dessins d'enfants / / Ernesto Girondo, Gabino González-Diez [[electronic resource]] |
| Autore | Girondo Ernesto |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xii, 298 pages) : digital, PDF file(s) |
| Disciplina | 515.93 |
| Collana | London Mathematical Society student texts |
| Soggetto topico |
Riemann surfaces
Dessins d'enfants (Mathematics) |
| ISBN |
1-107-08470-9
1-107-22435-7 1-280-48433-0 9786613579317 1-139-20529-3 1-139-20311-8 1-139-20169-7 1-139-20609-5 1-139-20451-3 1-139-04891-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; LONDON MATHEMATICAL SOCIETY STUDENT TEXTS; Title; Copyright; Dedication; Contents; Preface; 1 Compact Riemann surfaces and algebraic curves; 1.1 Basic definitions; 1.1.1 Riemann surfaces - examples; 1.1.2 Morphisms of Riemann surfaces; 1.1.3 Differentials; 1.2 Topology of Riemann surfaces; 1.2.1 The topological surface underlying a compact Riemann surface; 1.2.2 The fundamental group; 1.2.3 The Euler-Poincaré characteristic; 1.2.4 The Riemann-Hurwitz formula for morphisms to the sphere; 1.2.6 Ramified coverings
1.2.7 Auxiliary results about the compactification of Riemann surfaces and extension of maps1.3 Curves, function fields and Riemann surfaces; 1.3.1 The function field of a Riemann surface; 1.3.2 Manipulating generators of a function field; 2 Riemann surfaces and discrete groups; 2.1 Uniformization; 2.1.1 PSL(2,R) as the group of isometries of hyperbolic space; 2.1.2 Groups uniformizing Riemann surfaces of genus g = 2; 2.2 The existence of meromorphic functions; 2.2.1 Existence of functions in genus g = 1; 2.2.2 Existence of functions in genus g = 2; 2.3 Fuchsian groups 2.4 Fuchsian triangle groups2.4.1 Triangles in hyperbolic space; 2.4.2 Reflections; 2.4.3 Construction of triangle groups; 2.4.4 The modular group PSL(2,Z); 2.5 Automorphisms of Riemann surfaces; 2.5.1 The action of the automorphism group on the function field; 2.5.2 Uniformization of Klein's curve of genus three; 2.6 The moduli space of compact Riemann surfaces; 2.6.1 The moduli space M1; 2.6.2 The moduli space Mg for g > 1; 2.7 Monodromy; 2.7.1 Monodromy and Fuchsian groups; 2.7.2 Characterization of a morphism by its monodromy; 2.8 Galois coverings; 2.9 Normalization of a covering of P1 2.9.1 The covering group of the normalization3 Belyi's Theorem; 3.1 Proof of part (a) => (b) of Belyi's Theorem; 3.1.1 Belyi's second proof of part (a) => (b); 3.2 Algebraic characterization of morphisms; 3.3 Galois action; 3.4 Points and valuations; 3.4.1 Galois action on points; 3.5 Elementary invariants of the action of Gal(C); 3.6 A criterion for definability over Q; 3.6.1 Proof of part (b) => (a) of Belyi's Theorem; 3.7 Proof of the criterion for definibility over Q; 3.7.1 Specialization of transcencendental coefficients; 3.7.2 Infinitesimal specializations; 3.7.3 End of the proof 3.8 The field of definition of Belyi functions4 Dessins d'enfants; 4.1 Definition and first examples; 4.1.1 The permutation representation pair of a dessin; 4.2 From dessins d'enfants to Belyi pairs; 4.2.1 The triangle decomposition associated to a dessin; 4.2.2 The Belyi function associated to a dessin; 4.3 From Belyi pairs to dessins; 4.3.1 The monodromy of a Belyi pair; 4.4 Fuchsian group description of Belyi pairs; 4.4.1 Uniform dessins; 4.4.2 Automorphisms of a dessin; 4.4.3 Regular dessins; 4.5 The action of Gal(Q) on dessins d'enfants; 4.5.1 Faithfulness on dessins of genus 0 4.5.2 Faithfulness on dessins of genus 1 |
| Altri titoli varianti | Introduction to Compact Riemann Surfaces & Dessins d'Enfants |
| Record Nr. | UNINA-9910461550103321 |
Girondo Ernesto
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to compact Riemann surfaces and dessins d'enfants / / Ernesto Girondo, Gabino González-Diez [[electronic resource]]
| Introduction to compact Riemann surfaces and dessins d'enfants / / Ernesto Girondo, Gabino González-Diez [[electronic resource]] |
| Autore | Girondo Ernesto |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2012 |
| Descrizione fisica | 1 online resource (xii, 298 pages) : digital, PDF file(s) |
| Disciplina | 515.93 |
| Collana | London Mathematical Society student texts |
| Soggetto topico |
Riemann surfaces
Dessins d'enfants (Mathematics) |
| ISBN |
1-107-08470-9
1-107-22435-7 1-280-48433-0 9786613579317 1-139-20529-3 1-139-20311-8 1-139-20169-7 1-139-20609-5 1-139-20451-3 1-139-04891-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; LONDON MATHEMATICAL SOCIETY STUDENT TEXTS; Title; Copyright; Dedication; Contents; Preface; 1 Compact Riemann surfaces and algebraic curves; 1.1 Basic definitions; 1.1.1 Riemann surfaces - examples; 1.1.2 Morphisms of Riemann surfaces; 1.1.3 Differentials; 1.2 Topology of Riemann surfaces; 1.2.1 The topological surface underlying a compact Riemann surface; 1.2.2 The fundamental group; 1.2.3 The Euler-Poincaré characteristic; 1.2.4 The Riemann-Hurwitz formula for morphisms to the sphere; 1.2.6 Ramified coverings
1.2.7 Auxiliary results about the compactification of Riemann surfaces and extension of maps1.3 Curves, function fields and Riemann surfaces; 1.3.1 The function field of a Riemann surface; 1.3.2 Manipulating generators of a function field; 2 Riemann surfaces and discrete groups; 2.1 Uniformization; 2.1.1 PSL(2,R) as the group of isometries of hyperbolic space; 2.1.2 Groups uniformizing Riemann surfaces of genus g = 2; 2.2 The existence of meromorphic functions; 2.2.1 Existence of functions in genus g = 1; 2.2.2 Existence of functions in genus g = 2; 2.3 Fuchsian groups 2.4 Fuchsian triangle groups2.4.1 Triangles in hyperbolic space; 2.4.2 Reflections; 2.4.3 Construction of triangle groups; 2.4.4 The modular group PSL(2,Z); 2.5 Automorphisms of Riemann surfaces; 2.5.1 The action of the automorphism group on the function field; 2.5.2 Uniformization of Klein's curve of genus three; 2.6 The moduli space of compact Riemann surfaces; 2.6.1 The moduli space M1; 2.6.2 The moduli space Mg for g > 1; 2.7 Monodromy; 2.7.1 Monodromy and Fuchsian groups; 2.7.2 Characterization of a morphism by its monodromy; 2.8 Galois coverings; 2.9 Normalization of a covering of P1 2.9.1 The covering group of the normalization3 Belyi's Theorem; 3.1 Proof of part (a) => (b) of Belyi's Theorem; 3.1.1 Belyi's second proof of part (a) => (b); 3.2 Algebraic characterization of morphisms; 3.3 Galois action; 3.4 Points and valuations; 3.4.1 Galois action on points; 3.5 Elementary invariants of the action of Gal(C); 3.6 A criterion for definability over Q; 3.6.1 Proof of part (b) => (a) of Belyi's Theorem; 3.7 Proof of the criterion for definibility over Q; 3.7.1 Specialization of transcencendental coefficients; 3.7.2 Infinitesimal specializations; 3.7.3 End of the proof 3.8 The field of definition of Belyi functions4 Dessins d'enfants; 4.1 Definition and first examples; 4.1.1 The permutation representation pair of a dessin; 4.2 From dessins d'enfants to Belyi pairs; 4.2.1 The triangle decomposition associated to a dessin; 4.2.2 The Belyi function associated to a dessin; 4.3 From Belyi pairs to dessins; 4.3.1 The monodromy of a Belyi pair; 4.4 Fuchsian group description of Belyi pairs; 4.4.1 Uniform dessins; 4.4.2 Automorphisms of a dessin; 4.4.3 Regular dessins; 4.5 The action of Gal(Q) on dessins d'enfants; 4.5.1 Faithfulness on dessins of genus 0 4.5.2 Faithfulness on dessins of genus 1 |
| Altri titoli varianti | Introduction to Compact Riemann Surfaces & Dessins d'Enfants |
| Record Nr. | UNINA-9910790469303321 |
|
Girondo Ernesto
|
||
| Cambridge : , : Cambridge University Press, , 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||