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

Authors
  • Cheltsov, Ivan
  • Shramov, Constantin
Type
Preprint
Publication Date
Dec 25, 2011
Submission Date
Oct 10, 2010
Source
arXiv
License
Yellow
External links

Abstract

We study the action of the Klein simple group G 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 G. As a by-product, we prove that X admits a Kahler-Einstein metric, and we construct a smooth polarized K3 surface of degree 22 with an action of the group G.

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