Cox rings of rational surfaces and redundant blow-ups

Abstract

We prove that the redundant blow-up preserves the finite generation of the Cox ring of a rational surface under a suitable assumption, and we study the birational structure of Mori dream rational surfaces via redundant blow-ups. It turns out that the redundant blow-up completely characterizes birational morphisms of Mori dream rational surfaces with anticanonical Iitaka dimension $0$. As an application, we construct new Mori dream rational surfaces with anticanonical Iitaka dimension $0$ and $-\infty$ of arbitrarily large Picard number.

16 pages. We have divided it into two parts and changed the title. This part will appear in Trans. Amer. Math. Soc

References in corpus (3)

• Big rational surfaces
• Canonical divisors on T-varieties
• Redundant blow-ups of rational surfaces with big anticanonical divisor

Cited by in corpus (1)

• Characterization of log del Pezzo pairs via anticanonical models