{"product_id":"the-calabi-problem-for-fano-threefolds-paperback-9781009193399","title":"The Calabi Problem for Fano Threefolds (Paperback \/ softback) 9781009193399","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Calabi Problem for Fano Threefolds\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book determines whether the general element of each family of Fano threefolds is K-polystable, a major problem in mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eCarolina Araujo (Author), Ana-Maria Castravet (Author), Ivan Cheltsov (Author), Kento Fujita (Author), Anne-Sophie Kaloghiros (Author), Jesus Martinez-Garcia (Author), Constantin Shramov (Author), Hendrik Süß (Author), Nivedita Viswanathan (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009193399, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 29 June 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e455 pages\u003cbr\u003e22.9 x 15.2 x 2.5 cm, 0.66 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'It is a difficult problem to check whether a given Fano variety is K-polystable. This book settles this problem for the general members of all the 105 deformation families of smooth Fano 3-folds. The book is recommended to anyone interested in K-stability and existence of Kähler-Einstein metrics on Fano varieties.' Caucher Birkar FRS, Tsinghua University and University of Cambridge\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAlgebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler–Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler–Einstein metric, containing many additional relevant results such as the classification of all Kähler–Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. K-stability\u003cbr\u003e 2. Warm-up: smooth del Pezzo surfaces\u003cbr\u003e 3. Proof of main theorem: known cases\u003cbr\u003e 4. Proof of main theorem: special cases\u003cbr\u003e 5. Proof of main theorem: remaining cases\u003cbr\u003e 6. The big table\u003cbr\u003e 7. Conclusion\u003cbr\u003e Appendix. Technical results used in proof of main theorem\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265396887832,"sku":"9781009193399","price":64.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781009193399i_beaf3c6a-e150-496e-89c6-8ed2e4cdbb55.jpg?v=1696791369","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-calabi-problem-for-fano-threefolds-paperback-9781009193399","provider":"Freshly Printed Books","version":"1.0","type":"link"}