Some non-finitely generated Cox rings

By Jos'e Luis Gonz'alez, Kalle Karu. Compositio Mathematica, 2014

68 citations recorded by the source corpus.

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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e41a17ab18367d785681755db2e9cc12d5e064ea

Citations in the corpus

• On blowing up the weighted projective plane (2016, unknown): “In fact, as we will see, the results of [8] even lead to the following:”