Three embeddings of the Klein simple group into the Cremona group of rank three

Ivan Cheltsov, Constantin Shramov

Research output: Contribution to journalArticlepeer-review

Abstract

We study the action of the Klein simple group PSL2( F7 ) consisting of 168 elements on two rational threefolds: the three-dimensional projective space and a smooth Fano threefold X of anticanonical degree 22 and index 1. We show that the Cremona group of rank three has at least three non-conjugate subgroups isomorphic to PSL2( F7 ). As a by-product, we prove that X admits a Kähler–Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group PSL2( F7 ).
Original languageEnglish
Pages (from-to)303-350
JournalTransformation Groups
Volume17
Issue number2
DOIs
Publication statusPublished - 2012

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