Open surfaces of small volume

Valery Alexeev; Wenfei Liu

Open surfaces of small volume

Algebraic Geometry 2017-02-01 v2

Authors: Valery Alexeev , Wenfei Liu

Abstract

We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$ . Both examples significantly improve known records.

Keywords

del pezzo surfaces log canonical geometry algebraic surfaces

Cite

@article{arxiv.1612.09116,
  title  = {Open surfaces of small volume},
  author = {Valery Alexeev and Wenfei Liu},
  journal= {arXiv preprint arXiv:1612.09116},
  year   = {2017}
}

Comments

v.2 adds a connection to the algebraic Montgomery-Yang problem. 15 pages, 4 figures

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