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arXiv · 2305.02943

Secants to the Kummer Variety and the minimal Cohomological Class

José Alejandro Aburto
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Abstract

We prove that, under certain conditions, the existence of a curve of $(m+2)$-secants to the Kummer variety of an indecomposable principally polarized abelian variety $X$, represents $m$-times the minimal cohomological class in $X$. In the case of $m=2$, we find an involution of such curve which proves that \(X\) is a Prym variety by results of Krichever-Grushevsky. This continues the work of Beauville and Debarre, who asked about the relation between some geometric properties of abelian varieties in a way to obtain a stratification of its moduli space.

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José Alejandro Aburto. 2023-05-04. Secants to the Kummer Variety and the minimal Cohomological Class. https://arxiv.org/abs/2305.02943

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