Format:
Online-Ressource (digital)
ISBN:
9783540705192
Series Statement:
SpringerLink
Content:
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.
Content:
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.
Note:
Includes bibliographical references and index
Additional Edition:
ISBN 9783540705185
Additional Edition:
Buchausg. u.d.T. Olsson, Martin C. Compactifying moduli spaces for Abelian varieties Berlin : Springer, 2008 ISBN 9783540705185
Language:
English
Subjects:
Mathematics
Keywords:
Abelsche Mannigfaltigkeit
;
Modulraum
;
Kompaktifizierung
;
Abelsche Mannigfaltigkeit
;
Modulraum
;
Kompaktifizierung
DOI:
10.1007/978-3-540-70519-2
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Olsson, Martin C.
Author information:
Morel, Jean-Michel 1953-
