2014/09/08 by Naichung Conan Leung, Leung, Naichung Conan, Jiajin Zhang +1
Mathematics · #14J26 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14J26 #msc:14M15
paper · pdf · doi:10.48550/arxiv.1409.2325
17 pages. Comments are welcome!
arxiv created 2014/09/08 · openalex publication_date 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.