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

Shin-Yao Jow; Adrien Sauvaget; Hacen Zelaci

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

Algebraic Geometry 2017-01-20 v2

Authors: Shin-Yao Jow , Adrien Sauvaget , Hacen Zelaci

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.

Keywords

principally polarized abelian variety m-minimal curve stable pair abelian variety family locus dimension

Cite

@article{arxiv.1611.02868,
  title  = {On the principally polarized abelian varieties that contain m-minimal curves},
  author = {Shin-Yao Jow and Adrien Sauvaget and Hacen Zelaci},
  journal= {arXiv preprint arXiv:1611.02868},
  year   = {2017}
}

Comments

9 pages. This paper has been written after the summer school PRAGMATIC

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

Abstract

Keywords

Cite

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