On the Cox ring of P^2 blown up in points on a line

Abstract

We show that the blow-up of P^2 in n points on a line has finitely generated Cox ring. We give explicit generators for the ring and calculate its defining ideal of relations.

7 pages, Final version, to appear in Math. Scand

References in corpus (3)

• Big rational surfaces
• The Cox ring of an algebraic variety with torus action
• Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

Cited by in corpus (1)

• Big rational surfaces