## Some non-finitely generated Cox rings

This page accompanies the article Some non-finitely generated Cox rings by Jose Gonzalez and Kalle Karu, to appear in Compositio Mathematica.

Below are two lists of projective planes P(a,b,c) whose blowups
at the unit element t_{0} in the big torus does not have a finitely generated
Cox ring:

- 6814 examples with a,b,c at most
N=100. (400KB file)

- 80133 examples with a,b,c at
most N=200. (5MB file)

Abstract: We give a large family of weighted projective planes, blown up at a smooth point, that do not have finitely generated Cox rings. We then use the method of Castravet and Tevelev to prove that the moduli space M

_{0,n}of stable n-pointed genus zero curves does not have a finitely generated Cox ring if n is at least 13.