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Cox rings of rational surfaces and flag varieties of ADE-types
- Publication Year :
- 2014
-
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.<br />Comment: 17 pages. Comments are welcome!
- Subjects :
- Mathematics - Algebraic Geometry
14J26, 14M15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1409.2325
- Document Type :
- Working Paper