Cremona transformations, surface automorphisms and plane cubics
Algebraic Geometry
2010-07-28 v2 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0811.3038,
title = {Cremona transformations, surface automorphisms and plane cubics},
author = {Jeffrey Diller},
journal= {arXiv preprint arXiv:0811.3038},
year = {2010}
}
Comments
29 pages. Many changes, including a new title and the addition of an appendix (contributed by Igor Dolgachev) which carefully treats the group law for singular and reducible cubics. To appear in the Michigan Math Journal