Rational surface automorphisms with positive entropy (Q332180)

Let \(F: X\rightarrow X\) be an automorphism of a surface \(X\). The entropy of \(F\) is the logarithm of the spectral radius of NEWLINE\[NEWLINEF^*: H^2(X,\mathbb{Z})\rightarrow H^2(X,\mathbb{Z}).NEWLINE\]NEWLINE By [\textit{S. Cantat}, C. R. Acad. Sci., Paris, Sér. I, Math. 328, No. 10, 901--906 (1999; Zbl 0943.37021)], a surface admitting an automorphism with positive entropy is either a \(K3\) surface, an Enriques surface, a complex torus or a rational surface.NEWLINENEWLINEThe paper under review is the presentation of a very big family of automorphisms of rational surfaces with positive entropy. These automorphisms are obtained as resolutions of birational maps that preserve a cuspidal cubic in \(\mathbb{P}^2\).