## Moduli Spaces of Abelian Surfaces: Compactification, Degenerations, and Theta FunctionsThe 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 Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) |

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### Contents

Moduli spaces | 3 |

Torus embeddings and applications | 14 |

Toroidal compactification of A 1 p | 45 |

The boundary of A 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?polarization | 235 |

Polarizations on degenerate abelian surfaces | 245 |

The HorrocksMumford bundle | 274 |

Construction of the HorrocksMumford map | 281 |

Extension of the HorrocksMumford map to 41 5 | 298 |

Extension of the HorrocksMumford map to 4 1 5 | 305 |

333 | |

343 | |