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Compactifying Moduli Spaces for Abelian Varieties / by Martin C. Olsson; edited by J. -M. Morel, F. Takens, B. Teissier

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Berlin ; Heidelberg : Springer, 2008Description: Online-Ressource (digital)ISBN:
  • 9783540705192
Subject(s): Additional physical formats: 9783540705185 | Buchausg. u.d.T.: Compactifying moduli spaces for Abelian varieties. Berlin : Springer, 2008. VI, 278 S.DDC classification:
  • 516.353
  • 516.35
  • 510
  • 510
MSC: MSC: *14-02 | 14Kxx | 14K10 | 14K25 | 14A20 | 14M25 | 14F10RVK: RVK: SI 850LOC classification:
  • QA564-609
  • QA3
DOI: DOI: 10.1007/978-3-540-70519-2Online resources: Summary: A Brief Primer on Algebraic Stacks -- Preliminaries -- Moduli of Broken Toric Varieties -- Moduli of Principally Polarized Abelian Varieties -- Moduli of Abelian Varieties with Higher Degree Polarizations -- Level Structure.Summary: This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.PPN: PPN: 1647258006Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-LNM | ZDB-2-SMA
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