Higher genus curves in mathematical physics and arithmetic geometry : AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, January 8, 2016, Seattle, Washington / Andreas Malmendier, Tony Shaska, editors.

Format:

Book

Conference/Event

Contributor:

Malmendier, Andreas, 1976- editor.

Shaska, Tony, 1967- editor.

Conference Name:

AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry (2016 : Seattle, Wash.)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 703

Contemporary mathematics, 703 0271-4132

Language:

English

Subjects (All):

Arithmetical algebraic geometry--Congresses.

Arithmetical algebraic geometry.

Mathematical physics--Congresses.

Mathematical physics.

Physical Description:

1 online resource (234 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2018]

Summary:

This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington. Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics. The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic K3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.

Contents:

Cover

Title page

Contents

Preface

A lower bound for the number of finitely maximal _{ }-actions on a compact oriented surface

1. Introduction

2. Preliminaries

3. Bounding Actions by the Length of the Tail

4. A Lower Bound for _{ _{ }, }

References

Galois action on regular dessins d'enfant with simple group action

2. Quasi-platonic group actions and regular Belyi functions

3. The Galois action on quasi-platonic actions

4. Examples of Galois actions on quasi-platonic actions

Equations of Riemann surfaces with automorphisms

1. The main algorithm

2. Example: A genus 7 Riemann surface with 54 automorphisms

3. Selected results

On the field of moduli of superelliptic curves

3. Field of moduli of superelliptic curves

4. Superelliptic curves of genus at most 10

5. Tables of superelliptic curves of genus between 5 and 10

Minimal integral Weierstrass equations for genus 2 curves

2. Reduction of binary quintics and sextics

3. Julia quadratic of genus two curves with extra automorphisms

4. Minimal models of curves with extra involutions

5. Some heuristics for curves with extra involutions defined over Q

Acknowledgments

Rational points in the moduli space of genus two

2. A database of integral binary sextics

3. Heights of genus two curves

4. Genus 2 curves over C

5. Algebraic invariants

6. Automorphisms

7. Genus 2 curves defined over Q

8. Minimal discriminant for Weierstrass equations

9. Constructing the databases

Appendix A. Functions of the genus 2 package

Genus 2 package

Moduli Space

Creating the databases

Appendix B. Basic Invariants and relations among them

References.

Strong arithmetic mirror symmetry and toric isogenies

2. Hypersurfaces in toric varieties

3. Elliptic curves

4. Experimental evidence for strong mirror symmetry

5. Picard-Fuchs equations

Inose's construction and elliptic 3 surfaces with Mordell-Weil rank 15 revisited

3. Inose type surface for the Jacobian of a curve of genus 2

4. Fibration with two * fibers

Higher-order Weierstrass weights of branch points on superelliptic curves

2. Preliminaries and notation

3. A basis of holomorphic q-differentials

4. Weights of branch points

Poncelet's porism and projective fibrations

Introduction

1. Limits and Invariants

2. Monodromy of -gons

Extending Runge's method for integral points

2. Notation and definitions

3. Runge's method

4. Two consequences of the Nullstellensatz

5. Main theorem

6. Relation to Runge's method

7. Algebraic curves

8. Higher-dimensional varieties

Self-inversive polynomials, curves, and codes

2. Self-inversive polynomials

3. Superelliptic curves and self-inversive polynomials

4. Self-reciprocal polynomials and reduction theory

5. Self-reciprocal polynomials and codes

Acknowledgment

Syzygy divisors on Hurwitz spaces

2. Divisors on Hurwitz spaces

3. The generic splitting type

4. The divisor class of mu

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4674-X