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Universal torsors of Del Pezzo surfaces and homogeneous spaces

Ulrich Derenthal
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Abstract

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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Ulrich Derenthal. 2007-02-07. Universal torsors of Del Pezzo surfaces and homogeneous spaces. https://arxiv.org/abs/math/0604195

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