Mathematical Research Letters

Volume 15, Issue 1, January 2008 pp. 163-183.

Automorphism groups and anti-pluricanonical curves

Authors: De-Qi Zhang
Author institution: National University of Singapore

Summary: 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.

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