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 \(G\subset \mathrm {PGL}_{3}(\mathbb {C})\).
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This work has been supported by IBS-R003-D1, Institute for Basic Science in Korea.
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Sakovics, D. G-birational rigidity of the projective plane. European Journal of Mathematics 5, 1090–1105 (2019). https://doi.org/10.1007/s40879-018-0261-x
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DOI: https://doi.org/10.1007/s40879-018-0261-x