Moduli of bundles over rational surfaces and elliptic curves I: Simply laced cases
Moduli of bundles over rational surfaces and elliptic curves I: Simply laced cases
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DOI：
10.1112/jlms/jdp053
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
N. Leung;Jiajin Zhang
中科院分区：
文献类型：
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作者：
N. Leung;Jiajin Zhang
众所周知，9 − n次的del Pezzo曲面一一对应于椭圆曲线上的平坦En丛。在这篇文章中，我们在一个更广泛的有理曲面类上构造ADE-丛，我们称之为ADE-曲面，并将上述对应关系推广到椭圆曲线上的所有平坦G-丛，其中G是任何单缀、单、紧和单连通李群。在下文中，我们将在这些有理曲面上构造非单缀李群G的G-丛，并将上述对应扩展到非单缀情况。
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.