On the principally polarized abelian varieties with m-minimal curves
In this paper, we study principally polarized abelian varieties X of dimension g with a curve C such that the class of C is m times the
minimal class. 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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