{"product_id":"cremona-groups-and-the-icosahedron","title":"Cremona Groups and the Icosahedron","description":"\u003cp\u003e\u003cstrong\u003eCremona Groups and the Icosahedron\u003c\/strong\u003e focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold \u003ci\u003eV\u003c\/i\u003e5, and gives a proof of its A5-birational rigidity.\u003c\/p\u003e\u003cp\u003eThe authors explicitly describe many interesting A5-invariant subvarieties of \u003ci\u003eV\u003c\/i\u003e5, including A5-orbits, low-degree curves, invariant anticanonical \u003ci\u003eK\u003c\/i\u003e3 surfaces, and a mildly singular surface of general type that is a degree five cover of the diagonal Clebsch cubic surface. They also present two birational selfmaps of \u003ci\u003eV\u003c\/i\u003e5 that commute with A5-action and use them to determine the whole group of A5-birational automorphisms. As a result of this study, they produce three non-conjugate icosahedral subgroups in the Cremona group of rank 3, one of them arising from the threefold \u003ci\u003eV\u003c\/i\u003e5.\u003c\/p\u003e\u003cp\u003eThis book presents up-to-date tools for studying birational geometry of higher-dimensional varieties. In particular, it provides readers with a deep understanding of the biregular and birational geometry of \u003ci\u003eV\u003c\/i\u003e5.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":54261712879960,"sku":"9781482251593","price":210.8,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9781482251593.jpg?v=1769008525","url":"https:\/\/agendabookshop.com\/products\/cremona-groups-and-the-icosahedron","provider":"Agenda Bookshop","version":"1.0","type":"link"}