New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric Surfaces

Abstract

We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether the blow-up is a Mori Dream Space is equivalent to countably many planar interpolation problems. We state a conjecture which generalizes a theorem of Gonzalez and Karu. We give new examples and non-examples of Mori Dream Spaces among these blow-ups.

arXiv comment41 pages. 7 figures. The earlier proof of Proposition 5.1 was incomplete. The proof is now complete

References in corpus (2)

• On blowing up the weighted projective plane
• Reduction method for linear systems of plane curves with base fat points

Cited by in corpus (1)

• Mori Dream Spaces and blow-ups of weighted projective spaces