Prym varieties that are not isomorphic to Jacobian

TL;DR

This paper investigates Prym varieties arising from ramified double covers of complex curves with automorphisms of prime order, providing explicit constructions of those not isomorphic to Jacobians.

Contribution

It introduces explicit constructions of Prym varieties that are not isomorphic to Jacobians, expanding understanding of Prym varieties with automorphisms of prime order.

Findings

Constructed examples of Prym varieties not isomorphic to Jacobians

Utilized Galois theory for explicit constructions

Focused on ramified double covers with automorphisms of prime order p>2

Abstract

We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order $p>2$. Using Galois theory, we give an explicit constructions of Prym varieties that are not isomorphic to jacobians (even if one ignores the polarizations).