Automorphism groups and anti-pluricanonical curves

Details Automorphism groups and anti-pluricanonical curves Automorphism groups and anti-pluricanonical curves

2007-05-03

arxiv.org/abs/0705.0476v1

Mathematics

Algebraic Geometry

Mathematical Research Letters (to appear); 20 pages

Scientific paper

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 . Z (semi-direct product), 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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