Burkhardt Quartic, Barth Sextic, and the Icosahedron. (7th October 2017)

• Record Type: Journal Article
• Authors: Cheltsov, Ivan; Przyjalkowski, Victor; Shramov, Constantin
• Is Part Of: International mathematics research notices. Volume 2019:Number 12(2019)
• Page Start: 3683
• Page End: 3703
• Publication Date: 2017-10-07
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx204
• Languages: English
• ISSNs: 1073-7928

Abstract

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.