{"title":"Equivariant pliability of the projective space","authors":"Ivan Cheltsov, Arman Sarikyan","doi":"10.1007/s00029-023-00869-4","DOIUrl":null,"url":null,"abstract":"Abstract We classify finite subgroups $$G\\subset {\\textrm{PGL}}_4({\\mathbb {C}})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>⊂</mml:mo> <mml:msub> <mml:mtext>PGL</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> such that $${\\mathbb {P}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> is not G -birational to conic bundles and del Pezzo fibrations, and explicitly describe all G -Mori fibre spaces that are G -birational to $${\\mathbb {P}}^3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> for these subgroups.","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"742 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Selecta Mathematica-New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00029-023-00869-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We classify finite subgroups $$G\subset {\textrm{PGL}}_4({\mathbb {C}})$$ G⊂PGL4(C) such that $${\mathbb {P}}^3$$ P3 is not G -birational to conic bundles and del Pezzo fibrations, and explicitly describe all G -Mori fibre spaces that are G -birational to $${\mathbb {P}}^3$$ P3 for these subgroups.
期刊介绍：
Selecta Mathematica, New Series is a peer-reviewed journal addressed to a wide mathematical audience. It accepts well-written high quality papers in all areas of pure mathematics, and selected areas of applied mathematics. The journal especially encourages submission of papers which have the potential of opening new perspectives.
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