Cox rings of rational surfaces and redundant blow-ups

Hwang, DongSeon; Park, Jinhyung

doi:10.1090/tran/6611

Cox rings of rational surfaces and redundant blow-ups
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by DongSeon Hwang and Jinhyung Park PDF

Trans. Amer. Math. Soc. 368 (2016), 7727-7743 Request permission

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.

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