Moduli spaces of modules over even Clifford algebras and Prym varieties

TL;DR

This paper explores the relationship between moduli spaces of modules over even Clifford algebra sheaves and Prym varieties, establishing rational maps and birational equivalences, with applications to instanton and Higgs bundles.

Contribution

It constructs explicit rational maps connecting module moduli spaces over Clifford algebra sheaves to Prym varieties and demonstrates birationality in specific cases.

Findings

Established a rational map from module moduli spaces to Prym varieties.

Proved the rational map is birational in certain cases.

Derived a correspondence between instanton bundles and twisted Higgs bundles.

Abstract

A conic fibration has an associated sheaf of even Clifford algebras on the base. In this paper, we study the relation between the moduli spaces of modules over the sheaf of even Clifford algebras and the Prym variety associated to the conic fibration. In particular, we construct a rational map from the moduli space of modules over the sheaf of even Clifford algebras to the special subvarieties in the Prym variety, and check that the rational map is birational in some cases. As an application, we get an explicit correspondence between instanton bundles of minimal charge on cubic threefolds and twisted Higgs bundles on curves.