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European Journal of Mathematics

, Volume 5, Issue 3, pp 1090–1105 | Cite as

G-birational rigidity of the projective plane

  • Dmitrijs SakovicsEmail author
Research Article

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 \(G\subset \mathrm {PGL}_{3}(\mathbb {C})\).

Keywords

Cremona group Birational rigidity Minimal surfaces 

Mathematics Subject Classification

14E07 14J45 20C25 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Geometry and PhysicsInstitute for Basic Science (IBS)PohangKorea

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