On isogenies of Prym varieties

TL;DR

This paper extends classical theorems to semi-canonical curves and demonstrates that, under certain conditions, generic Prym varieties are not isogenous to other distinct Prym varieties, revealing new insights into their structure.

Contribution

It generalizes the Babbage-Enriques-Petri theorem for semi-canonical curves and establishes non-isogeny results for generic Prym varieties in specific subvarieties.

Findings

Extended classical theorem to semi-canonical curves

Proved generic Prym varieties are not isogenous to others under mild conditions

Provided new structural insights into Prym varieties

Abstract

We prove an extension of the Babbage-Enriques-Petri theorem for semi-canonical curves. We apply this to show that the Prym variety of a generic element of a codimension $k$ subvariety of $\mathcal{R}_{g}$ is not isogenous to another distinct Prym variety, under some mild assumption on $k$.