{"product_id":"k-stability-of-fano-varieties-hardback-9781009538770","title":"K-stability of Fano Varieties (Hardback) 9781009538770","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eK-stability of Fano Varieties\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe first book to provide a comprehensive and self-contained algebraic treatment of the emerging field of K-stability.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eChenyang Xu (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009538770, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 April 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e423 pages\u003cbr\u003e22.9 x 15.2 x 2.7 cm, 0.72 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donaldson conjecture was resolved. This is the first book to give a comprehensive algebraic treatment of this emerging field. It introduces all the notions of K-stability that have been used over the development of the subject, proves their equivalence, and discusses newly developed theory, including several new proofs for existing theorems. Aiming to be as self-contained as possible, the text begins with a chapter covering essential background knowledge, and includes exercises throughout to test understanding. Written by an author at the forefront of developments in the area, it will be a source of inspiration for graduate students and researchers who work in algebraic geometry.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Notion and conventions\u003cbr\u003e Preliminaries\u003cbr\u003e 1. Higher dimensional geometry background\u003cbr\u003e 2. K-stability via test configurations\u003cbr\u003e 3. K-stability via filtrations\u003cbr\u003e 4. K-stability via valuations\u003cbr\u003e 5. Higher rank finite generation\u003cbr\u003e 6. Reduced stability\u003cbr\u003e 7. K-moduli stack\u003cbr\u003e 8. K-moduli space\u003cbr\u003e 9. Positivity of the CM line bundle\u003cbr\u003e Appendix A. Solutions to exercises\u003cbr\u003e Bibliography\u003cbr\u003e Glossary\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":"Brand New","offer_id":52470036365592,"sku":"9781009538770","price":100.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009538770i.jpg?v=1785629113","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/k-stability-of-fano-varieties-hardback-9781009538770","provider":"Freshly Printed Books","version":"1.0","type":"link"}