# American Institute of Mathematical Sciences

2021, 17: 267-284. doi: 10.3934/jmd.2021008

## Tri-Coble surfaces and their automorphisms

 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

Received  April 2020 Revised  January 28, 2021 Published  May 2021

Fund Project: This work was supported by NSF grant DMS-1912476 and a Sloan Research Fellowship

We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The surfaces in question, which we term tri-Coble surfaces, are blow-ups of $\mathbb P^2$ 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 $1$ weak del Pezzo surfaces.

Citation: John Lesieutre. Tri-Coble surfaces and their automorphisms. Journal of Modern Dynamics, 2021, 17: 267-284. doi: 10.3934/jmd.2021008
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##### References:
A configuration of three tangent quadrics. In this case, two of the quadrics are tangent along an entire curve
$\tau_ \mathbf p$ fixes $\mathbf q$ and $\tau_ \mathbf q$ fixes $\mathbf p$ if and only if $S$ is tangent to four conic curves. According to Lemma 2.6, this is possible only if $S$ is tangent to a conic surface, which means that $S_{ \mathbf p \mathbf q}$ is a Coble surface
The action of $G$ on $\Delta$
The set ${\rm{Conv}}(\Lambda)$
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