Surfaces

Abstract

. Let Cox( S r ) be the homogeneous coordinate ring of the blow-up S r of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r . We prove that for r ∈ { 6 , 7 } , Proj(Cox( S r )) can be embedded into G r /P r , where G r is an algebraic group with root system given by the primitive Picard lattice of S r and P r ⊂ G r is a certain maximal parabolic subgroup.