On the Singularities of Degenerate Abelian Varieties

Joseph Tenini

paper

On the Singularities of Degenerate Abelian Varieties

arXiv:1401.0516

Abstract

In 2002, Alexeev provided a modular interpretation for the toroidal compactification of $A_{g}$ for the 2nd Voronoi fan. In this paper we show that pairs $(X, Θ)$ in the boundary of this moduli space are semi-log canonical, the analog of log canonical in the non-normal setting. This extends the result of Koll $a ˊ$ r stating that principally polarized abelian pairs $(X, Θ)$ are log canonical.

5 pages

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