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On the principally polarized abelian varieties with m-minimal curves
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On the principally polarized abelian varieties with m-minimal curves

Shin-Yao Jow, Adrien Sauvaget and Hacen Zelaci
Matematiche, Vol.72(2), pp.87-98
2017
DOI: https://doi.org/10.4418/2017.72.2.7

Abstract

Abelian varieties Jacobian Minimal class Moduli space of abelian varieties Prym variety Information Systems Mathematics (miscellaneous) Applied Mathematics
In this paper, we study principally polarized abelian varieties X of dimension g with a curve v: C → X such that the class of C is m times the minimal class. In [11], Welters introduced the formalism of complementary 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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