Moduli spaces of flat tori and elliptic hypergeometric functions / Sélim Ghazouani, Luc Pirio.

Format:

Book

Author/Creator:

Ghazouani, Sélim, author.

Pirio, Luc, author.

Series:

Mémoire (Société mathématique de France) ; 0249-633X nouv. sér., no. 164.

Mémoires de la Société Mathématique de France, 0249-633X ; Nouvelle série, Numéro 164

Language:

English

French

Subjects (All):

Geometry, Algebraic.

Moduli theory.

Foliations (Mathematics).

Hyperbolic spaces.

Curves, Elliptic.

Sheaf theory.

Singularities (Mathematics).

Functions, Theta.

Physical Description:

viii, 183 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, 2020.

Language Note:

Begins with "Abstract" in English and French.

Summary:

"... Our starting point is an explicit formula for flat metrics with cone singularities on elliptic curves, in terms of theta functions. From this, we deduce an explicit description of Veech's foliation: at the level of the Torelli space of n-marked elliptic curves, it is given by an explicit affine first integral. From the preceding result, one determines exactly which leaves of Veech's foliation are closed subvarieties of the moduli space M1,n of n-marked elliptic curves. We also give a local explicit expression, in terms of hypergeometric elliptic integrals, for the Veech map by means of which is defined the complex hyperbolic structure of a leaf."--Page iii.

Contents:

Introduction

Notation and preliminary material

Twisted (co)homology and integrals of hypergeometric type

An explicit expression for Veech's map and some consequences

Flat tori with two cone points

Some explicit computations and a proof of Veech's volume conjecture when g = 1 and n = 2

Appendix A. 1-dimensional complex hyperbolic conifolds

Appendix B. Manin connection associated to Veech's map.

Notes:

Includes bibliographical references (pages 177-183) and index.

ISBN:

9782856299227

2856299229

OCLC:

1196187537