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 t0 in the big torus does not have a finitely generated
Here is the C program
that produced these lists. (Change N at the beginning, compile with
"gcc -lm pplanes1.c" if using Linux.)
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 M0,n of stable n-pointed genus zero curves does not have a finitely generated Cox ring if n is at least 13.