A compactification of the moduli scheme of abelian varieties

2001/07/23 by Iku Nakamura, Nakamura, Iku
Mathematics · #14J10 #14K10 #14K25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J10 #msc:14K10 #msc:14K25

paper · pdf · doi:10.48550/arxiv.math/0107158

20 pages in latex2e, no figures

arxiv created 2001/07/23 · arxiv updated 2009/11/30

Abstract

We construct a canonical compactification SQ^toric_g,K of the moduli of abelian varieties over Z[ζ_N, 1/N] where ζ_N is a primitive N-th root of unity. This is very similar to, but slightly diferent from the compactification constructed by the author in Inventiones vol. 136 (1999). Any degenerate abelian scheme on the boundary of SQ^toric_g,K is reduced and singular and it is one of the stable quasi-abelian varieties introduced by Alexeev and the author (Tohoku J. 1999).

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