Cremona transformations, surface automorphisms and plane cubics

Details Cremona transformations, surface automorphisms and plane cubics Cremona transformations, surface automorphisms and plane cubics

2008-11-19

arxiv.org/abs/0811.3038v2

Mathematics

Algebraic Geometry

29 pages. Many changes, including a new title and the addition of an appendix (contributed by Igor Dolgachev) which carefully

Scientific paper

We give a method for constructing many examples of automorphisms with positive entropy on rational complex surfaces. The general idea is to begin with a quadratic Cremona transformation that fixes a reduced cubic curve and then use the group structure on the cubic to understand when the indeterminacy and exceptional behavior of the transformation may be eliminated by repeated blowing up.

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