A compactification of the moduli scheme of abelian varieties
Abstract
Description
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).
20 pages in latex2e, no figures
20 pages in latex2e, no figures