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

Abstract

Building on the work of Goto, Nishida and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with n punctures is not a Mori Dream Space for n>133. This answers the question of Hu and Keel.

Improved exposition; published version

Cited by in corpus (17)

• Some non-finitely generated Cox rings
• On blowing up the weighted projective plane
• On torus actions of higher complexity
• On the biregular geometry of the Fulton-MacPherson compactification
• Mori Dream Spaces and blow-ups of weighted projective spaces
• Positivity of divisors on blown-up projective spaces, II
• A simplicial approach to effective divisors in ${\overline{M}}_{0,n}$
• Permutohedral complexes and rational curves with cyclic action
• Hyperelliptic classes are rigid and extremal in genus two
• Projective linear configurations via non-reductive actions
• Birational geometry of moduli spaces of configurations of points on the line
• Cox rings over nonclosed fields
• Reductive quotients of klt singularities
• On the Cox ring of blowing up the diagonal
• Birational geometry of blow-ups of projective spaces along points and lines
• Constructing non-Mori Dream Spaces from negative curves
• A remark on the Cox ring of ${\overline{M}}_{0,n}$