Open surfaces of small volume

Abstract

We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48983$ 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.

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

References in corpus (1)

• Characterization of Kollár surfaces

Cited by in corpus (2)

• Some remarks on the volume of log varieties
• Log surfaces of Picard rank one from four lines in the plane