Translator Disclaimer
VOL. 58 | 2010 Another canonical compactification of the moduli space of abelian varieties

Abstract

We construct a canonical compactification $SQ_{g,K}^{\mathrm{toric}}$ of the moduli space $A_{g,K}$ of abelian varieties over $\mathbf{Z}[\zeta_N, 1/N]$ by adding certain reduced singular varieties along the boundary of $A_{g,K}$, where $K$ is a symplectic finite abelian group, $N$ is the maximal order of elements of $K$, and $\zeta_N$ is a primitive $N$-th root of unity. In [18] a canonical compactification $SQ_{g,K}$ of $A_{g,K}$ 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 : $SQ_{g,K}^{\mathrm{toric}} \to SQ_{g,K}$. In particular, the normalizations of $SQ_{g,K}^{\mathrm{toric}}$ and $SQ_{g,K}$ 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

PROCEEDINGS ARTICLE
67 PAGES


SHARE
Back to Top