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Cox rings of rational surfaces and flag varieties of ADE types

Conan Leung The Chinese University of Hong Kong Jiajin Zhang Sichuen University

mathscidoc:1608.01038

Comm Analy Geom, 23, (2), 293-317, 2015
The Cox rings of del Pezzo surfaces are closely related to the Lie groups En. In this paper, we generalize the definition of Cox rings to G-surfaces defined by us earlier, where the Lie groups G = An,Dn or En. We show that the Cox ring of a G-surface S is closely related to an irreducible representation V of G, and is generated by degree one elements. The Proj of the Cox ring of S is a sub-variety of the orbit of the highest weight vector in V , and both are closed sub-varieties of P(V ) defined by quadratic equations. The GIT quotient of the Spec of such a Cox ring by a natural torus action is considered.
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@inproceedings{conan2015cox,
  title={Cox rings of rational surfaces and flag varieties of ADE types},
  author={Conan Leung, and Jiajin Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828213425351135515},
  booktitle={Comm Analy Geom},
  volume={23},
  number={2},
  pages={293-317},
  year={2015},
}
Conan Leung, and Jiajin Zhang. Cox rings of rational surfaces and flag varieties of ADE types. 2015. Vol. 23. In Comm Analy Geom. pp.293-317. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160828213425351135515.
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