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Kac–Moody  affine Ek-bundles over elliptic curves and del Pezzo surfaces with singularities of type A

Conan Leung The Chinese University of Hong Kong Jiajin Zhang Sichuen University Mang Xu Southwest Jiaotong University

mathscidoc:1608.01043

Mathematische Annalen, 352, 805-828, 2012
Given an elliptic curve , flat Ek-bundles over  are in one-to-one correspondence with smooth del Pezzo surfaces of degree 9 − k containing  as an anti-canonical curve. This correspondence was generalized to Lie groups of any type. In this article, we show that there is a similar correspondence between del Pezzo surfaces of degree 0 with an Ad-singularity containing  as an anti-canonical curve and Kac–Moody  Ek-bundles over  with k = 8−d. In the degenerate case where surfaces are rational elliptic surfaces, the corresponding  Ek-bundles over  can be reduced to Ek-bundles.
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@inproceedings{conan2012kac–moody,
  title={Kac–Moody  affine Ek-bundles over elliptic curves and del Pezzo surfaces with singularities of type A },
  author={Conan Leung, Jiajin Zhang, and Mang Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828215038987024522},
  booktitle={Mathematische Annalen},
  volume={352},
  pages={805-828},
  year={2012},
}
Conan Leung, Jiajin Zhang, and Mang Xu. Kac–Moody  affine Ek-bundles over elliptic curves and del Pezzo surfaces with singularities of type A . 2012. Vol. 352. In Mathematische Annalen. pp.805-828. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828215038987024522.
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