A Galois-theoretic approach to Kanev's correspondence

TL;DR

This paper explores Galois coverings with finite groups, analyzing associated correspondences to compute invariants and construct new Prym-Tyurin varieties, advancing understanding of their algebraic and geometric properties.

Contribution

It introduces a Galois-theoretic framework to relate Schur and Kanev correspondences and computes their invariants, leading to new examples of Prym-Tyurin varieties.

Findings

Relation between Schur and Kanev correspondences established

Invariants of the correspondences computed

New Prym-Tyurin varieties constructed

Abstract

Let $G$ be a finite group, $\Lambda$ an absolutely irreducible $\Z[G]$-module and $w$ a weight of $\Lambda$. To any Galois covering with group $G$ we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants. Using this, we give some new examples of Prym-Tyurin varieties.