Mathematical Research Letters
Volume 15 (2008)
Automorphism groups and anti-pluricanonical curves
Pages: 163 – 183
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.