Algebraic cycles on Prym varieties

TL;DR

This paper generalizes the concept of tautological rings to Prym varieties, showing that under certain conditions, special subvarieties are algebraically equivalent and their classes are within the tautological ring.

Contribution

It introduces a new framework extending tautological rings to Prym varieties and proves algebraic equivalence of certain subvarieties within this context.

Findings

Special subvarieties of Prym varieties are algebraically equivalent.

Their classes belong to the generalized tautological ring.

The generalization applies under specific hypotheses.

Abstract

This article proposes a generalization of tautological rings introduced by Beauville and Moonen for Jacobians. The main result is that, under certain hypotheses, the special subvarieties of Prym varieties are algebraically equivalent and their classes belong to the tautological ring.