Cox rings of rational surfaces and redundant blow-ups

DongSeon Hwang; Jinhyung Park

Cox rings of rational surfaces and redundant blow-ups

Algebraic Geometry 2014-11-17 v2

Authors: DongSeon Hwang , Jinhyung Park

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.

Keywords

Cox rings rational surfaces redundant blow-ups finite generation Mori dream surfaces birational morphisms anticanonical Iitaka dimension Picard number

Cite

@article{arxiv.1303.2274,
  title  = {Cox rings of rational surfaces and redundant blow-ups},
  author = {DongSeon Hwang and Jinhyung Park},
  journal= {arXiv preprint arXiv:1303.2274},
  year   = {2014}
}

Comments

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

Cox rings of rational surfaces and redundant blow-ups

Abstract

Keywords

Cite

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