Moduli Spaces of Abelian Surfaces: Compactification, Degenerations and Theta Functions

Description

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) Introduction I Compactified moduli spaces 1 Moduli spaces 2 Torus embeddings and applications 3 Toroidal compactification of A(1, p) 4 The boundary of A*(1, p) 5 Humbert surfaces and scaffoldings 6 The Satake compactification II Degenerations of abelian surfaces 1 Mumford’s construction 2 The basic construction for surfaces 3 Degenerate abelian surfaces (the principally polarized case) 4 Degenerate abelian surfaces (the case of (1,p)-polarization) 5 Polarizations on degenerate abelian surfaces III The Horrocks-Mumford map 1 The Horrocks-Mumford bundle 2 Construction of the Horrocks-Mumford map 3 Extension of the Horrocks-Mumford map to A(1, 5) 4 Extension of the Horrocks-Mumford map to A* (1, 5) Bibliography Glossary of Notations Index