Continuous families of rational surface automorphisms with positive entropy

Abstract

For any k we construct k-parameter families of rational surface automorphisms with positive entropy. These are automorphisms of surfaces $${\mathcal{X}}$$ , which are constructed from iterated blowups over the projective plane. In certain cases we are able to determine the exact automorphism group of $${\mathcal{X}}$$ , as well as when two of these surfaces are inequivalent.