Cremona transformations, surface automorphisms and plane cubics
By Jeffrey Diller. 2008
60 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/78f93584729de76eeec4b381d490bd6c37677ec5
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Dynamical degrees of birational transformations of projective surfaces (2013, result): “one can prove the following properties as a corollary of our previous results, known facts on Pisot numbers (see [7]), and a systematic study of quadratic birational transformations of the plane (see [19] and §8): (a) The Golden mean l G is the smallest accumulation point in the set of Pisot numbers”
- Rational Surface Automorphisms with Positive Entropy (2010, background): “On the other hand, for any data τ̂ = (1, σ̂, κ̂), let Fτ̂ : Xτ̂ → Xτ̂ be an automorphism that Diller in [6] constructs from a single quadratic map preserving a cuspidal cubic.”