Compactification of the Prym map for non cyclic triple coverings

Details Compactification of the Prym map for non cyclic triple coverings Compactification of the Prym map for non cyclic triple coverings

2011-03-25

arxiv.org/abs/1103.4982v1

Mathematics

Algebraic Geometry

28 pages, 1 figure

Scientific paper

In a previous paper, the authors proved that the Prym variety of any non-cyclic etale triple cover of a smooth curve of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space of Jacobian varieties of dimension 2. We extend this map to a proper map of a certain moduli space of admissible $S_3$-covers of genus 7 to the moduli space of principally polarized abelian surfaces. The main result is that this map is finite surjective of degree 10.

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