Resumen de Moduli of bundles over rational surfaces and elliptic curves I: simply laced cases

Naichung Conan Leung, Jiajin Zhang

• It is well known that del Pezzo surfaces of degree 9 - n one-to-one correspond to flat En bundles over an elliptic curve. In this paper, we construct ADE-bundles over a broader class of rational surfaces that we call ADE-surfaces, and extend the above correspondence to all flat G-bundles over an elliptic curve, where G is any simply laced, simple, compact and simply connected Lie group. In what follows, we will construct G-bundles for a non-simply laced Lie group G over these rational surfaces, and extend the above correspondence to non-simply laced cases.