Cremona transformations, surface automorphisms and plane cubics

2008/11/19 by Jeffrey Diller, Diller, Jeffrey · 2 citations
Mathematics · #14E07 #14H52 #14J50 #37F99 #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0811.3038

openalex publication_date 2008/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Real Rational Surface Automorphisms : Positivity and Linearity
• Siegel Disks on Rational Surfaces

Related

• Continuous Families of Rational Surface Automorphisms with Positive Entropy
• Entropy of real rational surface automorphisms
• Real Rational Surface Automorphisms : Positivity and Linearity
• Entropy of real rational surface automorphisms: Actions on the Fundamental Groups
• Rational Surface Automorphisms with Positive Entropy