Q-abelian and $\mathbb Q$-Fano finite quotients of abelian varieties

Takahiro Shibata

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arXiv · 2112.09826

Q-abelian and $\mathbb Q$-Fano finite quotients of abelian varieties

Takahiro Shibata

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Abstract

We study finite quotients of abelian varieties (fqav for short) i.e. quotients of abelian varieties by finite groups. We show that Q-abelian varieties (i.e. fqav's with $\mathbb Q$-linearly trivial canonical divisors) are characterized by the existence of quasi\'etale polarized (or int-amplified) endomorphisms. We show that every fqav has a finite quasi\'etale cover by the product of an abelian variety and a $\mathbb Q$-Fano fqav. Using such coverings, we give a characterization of $\mathbb Q$-Fano fqav's, and show that $\mathbb Q$-Fano fqav's and Q-abelian varieties are ``building blocks'' of general fqav's.

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BibTeX RIS

Takahiro Shibata. 2021-12-18. Q-abelian and $\mathbb Q$-Fano finite quotients of abelian varieties. https://arxiv.org/abs/2112.09826

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