The trigonal construction in the ramified case

2019/02/01 by Lange, Herbert, Ortega, Angela
#14H30 #14H40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.00251

Abstract

To every double cover ramified in two points of a general trigonal curve of genus g, one can associate an étale double cover of a tetragonal curve of genus g+1. We show that the corresponding Prym varieties are canonically isomorphic as principally polarized abelian varieties.

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• Shimura curves in the Prym loci of ramified double covers
• Compactification of the Prym map for non cyclic triple coverings
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• Polarization types of isogenous Prym-Tyurin varieties