Tri-Coble surfaces and their automorphisms

Abstract

<p style="text-indent:20px;">We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The surfaces in question, which we term <em>tri-Coble surfaces</em>, are blow-ups of <inline-formula><tex-math id="M1">\begin{document}$ \mathbb P^2$\end{document}</tex-math></inline-formula> at 12 points which have contractions down to three different Coble surfaces. The automorphisms arise as compositions of lifts of Bertini involutions from certain degree <inline-formula><tex-math id="M2">\begin{document}$1$\end{document}</tex-math></inline-formula> weak del Pezzo surfaces.