Universal torsors of Del Pezzo surfaces and homogeneous spaces

Details Universal torsors of Del Pezzo surfaces and homogeneous spaces Universal torsors of Del Pezzo surfaces and homogeneous spaces

2006-04-10

arxiv.org/abs/math/0604195v3

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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

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