Absolutely simple Prymians of trigonal curves

TL;DR

This paper constructs explicit examples of absolutely simple Prym varieties that are not isomorphic to Jacobians of curves, using Galois Theory, expanding understanding of Prym varieties' structure.

Contribution

It provides explicit constructions of absolutely simple Prym varieties that are not Jacobians, utilizing Galois Theory, which was not previously demonstrated.

Findings

Explicit examples of absolutely simple Prym varieties

Prym varieties not isomorphic to Jacobians even ignoring polarizations

Application of Galois Theory to Prym variety construction

Abstract

Using Galois Theory, we construct explicitly absolutely simple (principally polarized) Prym varieties that are not isomorphic to jacobians of curves even if we ignore the polarizations. Our approach is based on the previous papers math/0610138 [math.AG] and math/0605028 [math.AG] .