On the Cox ring of Del Pezzo surfaces

Details On the Cox ring of Del Pezzo surfaces On the Cox ring of Del Pezzo surfaces

2006-03-04

arxiv.org/abs/math/0603111v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Let S_r be the blow-up of P^2 in r general points, i.e., a smooth Del Pezzo
surface of degree 9-r. For r <= 7, we determine the quadratic equations
defining its Cox ring explicitly. The ideal of the relations in Cox(S_8) is
calculated up to radical. As conjectured by Batyrev and Popov, all the
generating relations are quadratic.

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