On the Cox ring of Del Pezzo surfaces
Ulrich Derenthal
Abstract
Let Sr be the blow-up of P2 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(S8) is calculated up to radical. As conjectured by Batyrev and Popov, all the generating relations are quadratic.
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