Finite quasisimple groups acting on rationally connected threefolds

Jérémy Blanc; Ivan Cheltsov; Alexander Duncan; Yuri  Prokhorov

Finite quasisimple groups acting on rationally connected threefolds

Jérémy Blanc, Ivan Cheltsov, Alexander Duncan, Yuri Prokhorov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: A5, PSL2(F7), A6, SL2(F8), A7, PSp4(F3), SL2(F7), 2.A5, 2.A6, 3.A6 or 6.A6.

All of these groups with a possible exception of 2.A6 and 6.A6 indeed act on some rationally connected threefolds.

Original language	English
Journal	Mathematical Proceedings of The Cambridge Philosophical Society
Publication status	Accepted/In press - 28 Jul 2022

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1809.09226Accepted author manuscript, 488 KB

https://arxiv.org/abs/1809.09226

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title = "Finite quasisimple groups acting on rationally connected threefolds",

abstract = "We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: A5, PSL2(F7), A6, SL2(F8), A7, PSp4(F3), SL2(F7), 2.A5, 2.A6, 3.A6 or 6.A6.All of these groups with a possible exception of 2.A6 and 6.A6 indeed act on some rationally connected threefolds.",

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T1 - Finite quasisimple groups acting on rationally connected threefolds

AU - Blanc, Jérémy

AU - Cheltsov, Ivan

AU - Duncan, Alexander

AU - Prokhorov, Yuri

PY - 2022/7/28

Y1 - 2022/7/28

N2 - We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: A5, PSL2(F7), A6, SL2(F8), A7, PSp4(F3), SL2(F7), 2.A5, 2.A6, 3.A6 or 6.A6.All of these groups with a possible exception of 2.A6 and 6.A6 indeed act on some rationally connected threefolds.

AB - We show that the only finite quasi-simple non-abelian groups that can faithfully act on rationally connected threefolds are the following groups: A5, PSL2(F7), A6, SL2(F8), A7, PSp4(F3), SL2(F7), 2.A5, 2.A6, 3.A6 or 6.A6.All of these groups with a possible exception of 2.A6 and 6.A6 indeed act on some rationally connected threefolds.

M3 - Article

JO - Mathematical Proceedings of The Cambridge Philosophical Society

JF - Mathematical Proceedings of The Cambridge Philosophical Society

SN - 0305-0041

ER -

Finite quasisimple groups acting on rationally connected threefolds

Abstract

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