Burkhardt Quartic, Barth Sextic, and the Icosahedron. (7th October 2017) - Cheltsov, Ivan
Abstract: We study two rational Fano three-folds with an action of the icosahedral group $\mathfrak{A}_5$ . 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 $\mathfrak{A}_5$ -Fano varieties that are $\mathfrak{A}_5$ -birationally superrigid. This gives two new embeddings of the group $\mathfrak{A}_5$ into the space Cremona group.