Some non-finitely generated Cox rings

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

14 pages, 2 figures

References in corpus (1)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space

Cited by in corpus (8)

• On blowing up the weighted projective plane
• On torus actions of higher complexity
• Mori Dream Spaces and blow-ups of weighted projective spaces
• Positivity of divisors on blown-up projective spaces, II
• Permutohedral complexes and rational curves with cyclic action
• Birational geometry of moduli spaces of configurations of points on the line
• Infinitely generated symbolic Rees algebras over finite fields
• Higher-dimensional Losev-Manin spaces and their geometry