Counter-examples of high Clifford index to Prym-Torelli

TL;DR

This paper constructs examples of algebraic curves with high Clifford index where the Prym map fails to be injective on their étale double covers, revealing new insights into the Prym-Torelli problem.

Contribution

It provides explicit counterexamples of high Clifford index curves with non-injective Prym maps, advancing understanding of Prym-Torelli phenomena.

Findings

Existence of high Clifford index curves with non-injective Prym maps

Counterexamples for the Prym-Torelli problem at high Clifford index

Insights into the relationship between Clifford index and Prym map injectivity

Abstract

We give examples of curves of arbitrarily high Clifford index such that the Prym map is not injective at any of their \'etale double covers.