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arXiv · 1611.02868

On the principally polarized abelian varieties that contain m-minimal curves

Shin-Yao Jow·Adrien Sauvaget·Hacen Zelaci
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Abstract

In this paper, we study principally polarized abelian varieties $X$ of dimension $g$ that contain a curve $\nu:C\to X$ such that the class of $C$ is $m$ times the minimal class. Welters introduced the formalism of stable pairs to handle this problem in the case $m=2$. We generalize the results of Welters and construct families of principally polarized abelian varieties for any $m$ and compute the dimension of the locus of these abelian varieties.

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Shin-Yao Jow, Adrien Sauvaget, Hacen Zelaci. 2016-11-09. On the principally polarized abelian varieties that contain m-minimal curves. https://arxiv.org/abs/1611.02868

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