Vol. 11, No. 4, 2017

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
The degree of the Gauss map of the theta divisor

Giulio Codogni, Samuel Grushevsky and Edoardo Sernesi

Vol. 11 (2017), No. 4, 983–1001
Abstract

We study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. Thanks to this analysis, we obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus. We spell out this bound in several examples, and we use it to understand the local structure of isolated singular points. We further define a stratification of the moduli space of ppavs by the degree of the Gauss map. In dimension four, we show that this stratification gives a weak solution of the Schottky problem, and we conjecture that this is true in any dimension.

Keywords
Gauss map, principally polarised abelian varieties, Schottky problem, V-cycles, excess intersection formula
Mathematical Subject Classification 2010
Primary: 14K10
Secondary: 14C17, 14H42
Milestones
Received: 17 August 2016
Revised: 10 January 2017
Accepted: 11 February 2017
Published: 18 June 2017
Authors
Giulio Codogni
Dipartimento di Matematica e Fisica
Università Roma Tre
Largo San Leonardo Murialdo
I-00146 Rome
Italy
Samuel Grushevsky
Mathematics Department
Stony Brook University
Stony Brook, NY 11794-3651
United States
Edoardo Sernesi
Dipartimento di Matematica e Fisica
Università Roma Tre
Largo San Leonardo Murialdo
I-00146 Roma
Italy