On the embeddings of universal torsors over del Pezzo surfaces in the cones over flag varieties

Abstract

Following Skorobogatov and Serganova we construct the embeddings of universal torsors over del Pezzo surfaces in the cones over flag varieties, considered as the closed orbits in the projectivization of quasiminiscule representations. We give the approach that allows us to construct the embeddings of universal torsors over del Pezzo surfaces of the degree one. This approach uses the Mumford stability and slightly differs from the approach of the authors named above.