Compactification of the Prym map for non cyclic triple coverings

2011/03/25 by Lange, Herbert, Ortega, Angela
#14H30 #14H40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1103.4982

Abstract

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 S₃-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.

Related

• The fibres of the Prym map of étale cyclic coverings of degree 7
• Prym varieties of cyclic coverings
• Cyclic Coverings of genus 2 curves of Sophie Germain type
• Generic injectivity of the Prym map for double ramified coverings
• Pryms of ℤ₃×ℤ₃ coverings of genus 2 curves