{"product_id":"cremona-groups-and-the-icosahedron-ivan-cheltsov-9781482251593","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 A\u003csub\u003e5\u003c\/sub\u003e in them. The book surveys known facts about surfaces with an action of A\u003csub\u003e5\u003c\/sub\u003e, explores A\u003csub\u003e5\u003c\/sub\u003e-equivariant geometry of the quintic del Pezzo threefold \u003ci\u003eV\u003c\/i\u003e\u003csub\u003e5\u003c\/sub\u003e, and gives a proof of its A\u003csub\u003e5\u003c\/sub\u003e-birational rigidity.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe authors explicitly describe many interesting A\u003csub\u003e5\u003c\/sub\u003e-invariant subvarieties of \u003ci\u003eV\u003c\/i\u003e\u003csub\u003e5\u003c\/sub\u003e, including A\u003csub\u003e5\u003c\/sub\u003e-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\u003e\u003csub\u003e5\u003c\/sub\u003e that commute with A\u003csub\u003e5\u003c\/sub\u003e-action and use them to determine the whole group of A\u003csub\u003e5\u003c\/sub\u003e-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\u003e\u003csub\u003e5\u003c\/sub\u003e.\u003c\/p\u003e \u003cp\u003e\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\u003e\u003csub\u003e5\u003c\/sub\u003e.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Ivan Cheltsov, Constantin Shramov\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1482251590\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781482251593\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e CRC Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/21\/2015\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 528\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.95lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.20h x 6.20w x 1.20d","brand":"Ivan Cheltsov","offers":[{"title":"Hardcover","offer_id":43935729058047,"sku":"9781482251593","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/products\/img_28f1c50c-f9f4-4653-bff7-d2ddea1450a3.jpg?v=1681421488","url":"https:\/\/www.whiterainbookhouse.com\/products\/cremona-groups-and-the-icosahedron-ivan-cheltsov-9781482251593","provider":"WR Book House","version":"1.0","type":"link"}