Cox rings of rational surfaces and redundant blow-ups

2013/03/09 by DongSeon Hwang, Jinhyung Park, Hwang, DongSeon +1 · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1303.2274

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 -∞ of arbitrarily large Picard number.

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• Characterization of log del Pezzo pairs via anticanonical models

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