Moduli of bundles over rational surfaces and elliptic curves II: non-simply laced cases

TL;DR

This paper extends the correspondence between moduli spaces of flat G-bundles over elliptic curves and rational surfaces with G-configurations to non-simply laced Lie groups, generalizing previous results for simply laced groups.

Contribution

It establishes a natural identification between moduli spaces of flat G-bundles and rational surfaces with G-configurations for all Lie groups, including non-simply laced cases.

Findings

Identifies moduli space of flat G-bundles with rational surfaces containing the elliptic curve as an anti-canonical divisor.

Constructs Lie(G)-bundles over these rational surfaces.

Generalizes previous results from simply laced to non-simply laced Lie groups.

Abstract

For any non-simply laced Lie group $G$ and elliptic curve $\Sigma$, we show that the moduli space of flat $G$ bundles over $\Sigma$ can be identified with the moduli space of rational surfaces with $G$-configurations which contain $\Sigma$ as an anti-canonical curve. We also construct $Lie(G)$-bundles over these surfaces. The corresponding results for simply laced groups were obtained by the authors in another paper. Thus we have established a natural identification for these two kinds of moduli spaces for any Lie group $G$.