Taniguchi Lecture on Principal Bundles on Elliptic Fibrations

TL;DR

This paper explores the moduli space of principal G-bundles on elliptic fibrations using cameral covers and Prym varieties, highlighting connections to Hitchin systems and applications in string theory dualities.

Contribution

It provides a detailed description of the moduli space in terms of cameral covers, extending previous work with new examples and insights into Hitchin system integrability.

Findings

Description of moduli space via cameral covers and Prym varieties

Connections established between principal bundles and Hitchin systems

Applications to heterotic/F-theory duality

Abstract

In this talk we discuss the description of the moduli space of principal G-bundles on an elliptic fibration X-->S in terms of cameral covers and their distinguished Prym varieties. We emphasize the close relationship between this problem and the integrability of Hitchin's system and its generalizations. The discussion roughly parallels that of [D2], but additional examples are included and some important steps of the argument are illustrated. Some of the applications to heterotic/F-theory duality were described in the accompanying ICMP talk (hep-th/9802093).