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

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

2010-10-10

arxiv.org/abs/1010.1918v3

Mathematics

Algebraic Geometry

43 pages

Scientific paper

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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