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

• Autores: Naichung Conan Leung, Jiajin Zhang
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 3, 2009, págs. 750-770
• Idioma: inglés
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• Resumen

  • 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.