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

Following Skorobogatov and Serganova, we construct embeddings of universal torsors over del Pezzo surfaces in cones over flag varieties regarded as closed orbits in the projectivizations of quasi-miniscule representations. Our approach enables us to construct embeddings of universal torsors over del Pezzo surfaces of degree 1. This approach uses the notion of Mumford stability and differs slightly from that of the authors named above.