Cox rings of rational surfaces and flag varieties of ADE-types

Naichung Conan Leung; Jiajin Zhang

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arXiv · 1409.2325

Cox rings of rational surfaces and flag varieties of ADE-types

Naichung Conan Leung·Jiajin Zhang

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Abstract

The Cox rings of del Pezzo surfaces are closely related to the Lie groups E_n. In this paper, we generalize the definition of Cox rings to G- surfaces defined by us earlier, where the Lie groups G=A_n, D_n or E_n. We show that the Cox ring of a G-surface S is almost determined by an irreducible representation V of G, and is generated by degree one elements. The Proj of this ring is a sub-variety of the orbit of the highest weight vector in V, and both are closed sub-varieties of the projective space P(V) defined by quadratic equations.

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Naichung Conan Leung, Jiajin Zhang. 2014-09-08. Cox rings of rational surfaces and flag varieties of ADE-types. https://arxiv.org/abs/1409.2325

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