On the Singularities of Degenerate Abelian Varieties

Joseph Tenini

On the Singularities of Degenerate Abelian Varieties

Algebraic Geometry 2014-03-25 v2

Authors: Joseph Tenini

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 $(X,\Theta)$ 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 ${\'a}$ r stating that principally polarized abelian pairs $(X,\Theta)$ are log canonical.

Keywords

degenerate Abelian varieties singularities toroidal compactification moduli space semi-log canonical log canonical principally polarized Abelian pairs

Cite

@article{arxiv.1401.0516,
  title  = {On the Singularities of Degenerate Abelian Varieties},
  author = {Joseph Tenini},
  journal= {arXiv preprint arXiv:1401.0516},
  year   = {2014}
}

Comments

5 pages

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