Open Access
VOL. 58 | 2010 Another canonical compactification of the moduli space of abelian varieties
Chapter Author(s) Iku Nakamura
Editor(s) Iku Nakamura, Lin Weng
Adv. Stud. Pure Math., 2010: 69-135 (2010) DOI: 10.2969/aspm/05810069

Abstract

We construct a canonical compactification SQg,Ktoric of the moduli space Ag,K of abelian varieties over Z[ζN,1/N] by adding certain reduced singular varieties along the boundary of Ag,K, where K is a symplectic finite abelian group, N is the maximal order of elements of K, and ζN is a primitive N-th root of unity. In [18] a canonical compactification SQg,K of Ag,K was constructed by adding possibly non-reduced GIT-stable (Kempf-stable) degenerate abelian schemes. We prove that there is a canonical bijective finite birational morphism sq : SQg,KtoricSQg,K. In particular, the normalizations of SQg,Ktoric and SQg,K are isomorphic.

Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1213.14077
MathSciNet: MR2676158

Digital Object Identifier: 10.2969/aspm/05810069

Subjects:
Primary: 14J10 , 14K10 , 14K25

Rights: Copyright © 2010 Mathematical Society of Japan

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