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arXiv · 1712.01587

$G$-birational rigidity of the projective plane

Dmitrijs Sakovics
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Abstract

Given a surface $S$ and a finite group $G$ of automorphisms of $S$, consider the birational maps $S\dashrightarrow S'$ that commute with the action of $G$. This leads to the notion of a $G$-minimal variety. A natural question arises: for a fixed group $G$, is there a birational $G$-map between two different $G$-minimal surfaces? If no such map exists, the surface is said to be $G$-birationally rigid. This paper determines the $G$-rigidity of the projective plane for every finite subgroup $G\subset\mbox{PGL}_3\left(\mathbb{C}\right)$.

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Dmitrijs Sakovics. 2017-12-05. $G$-birational rigidity of the projective plane. https://arxiv.org/abs/1712.01587

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