Mathematical Research Letters

Volume 15 (2008)

Number 1

Automorphism groups and anti-pluricanonical curves

Pages: 163 – 183



De-Qi Zhang (National University of Singapore)


We show the existence of an anti-pluricanonical curve on every smooth projective rational surface $X$ which has an infinite group $G$ of automorphisms of either null entropy or of type $\Z \ltimes \Z$, provided that the pair $(X, G)$ is minimal. This was conjectured by Curtis T. McMullen (2005) and further traced back to Marat Gizatullin and Brian Harbourne (1987). We also prove (perhaps) the strongest form of the famous Tits alternative theorem.

Published 1 January 2008