Moscow Mathematical Journal

Volume 22, Issue 2, April–June 2022 pp. 225–237.

Smooth Quotients of Principally Polarized Abelian Varieties

Authors: Robert Auffarth (1) and Giancarlo Lucchini Arteche (1)
Author institution:(1) Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile

Summary:

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup $G\subseteq\mathrm{Aut}(A,\Theta)$ such that the quotient variety $A/G$ is smooth. We also give a complete classification of smooth quotients of Jacobians of curves.

2020 Math. Subj. Class. Primary: 14L30, 14K10; Secondary: 14H37, 14H40.

Keywords: Abelian varieties, principal polarizations, Jacobians of curves, smooth quotients, automorphisms.

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