Affine ADE bundles over complex surfaces with p_g=0

TL;DR

This paper constructs affine ADE Lie algebra bundles over complex surfaces with p_g=0, demonstrating their deformation properties and linking the geometry of the surface to bundle deformability.

Contribution

It introduces a method to construct affine ADE bundles over complex surfaces with p_g=0 and explores their deformation behavior, especially over Kodaira curves.

Findings

Bundles become trivial on each component after deformation

Existence of a canonical E_8-bundle over certain blowups of P^2

Surface geometry influences bundle deformability

Abstract

We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that p_g(X)=0. When X is a blowup of P^2 at nine points, there is a canonical E_8-bundle E over X. We show that the geometry of X can be reflected by the deformability of E.