Burkhardt Quartic, Barth Sextic, and the Icosahedron. (7th October 2017) - Cheltsov, Ivan; Przyjalkowski, Victor; Shramov, Constantin
Abstract: We study two rational Fano three-folds with an action of the icosahedral group A_5 . The first one is the famous Burkhardt quartic three-fold, and the second one is the double cover of the projective space branched in the Barth sextic surface. We prove that both of them are A_5 -Fano varieties that are A_5 -birationally superrigid. This gives two new embeddings of the group A_5 into the space Cremona group.