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

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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, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

 

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Contents

Moduli spaces
3
Torus embeddings and applications
14
Toroidal compactification of A1p
45
The boundary of A1 p
125
Humbert surfaces and scaffoldings
155
The Satake compactification
184
Mumfords construction
195
The basic construction for surfaces
204
Degenerate abelian surfaces the case of 1 ppolarization
235
Polarizations on degenerate abelian surfaces
245
The HorrocksMumford bundle
274
Construction of the HorrocksMumford map
281
Extension of the HorrocksMumford map to A15
298
Extension of the HorrocksMumford map to A15
305
Bibliography
333
Index
343

Degenerate abelian surfaces the principally polarized case
215

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