{"product_id":"the-calabi-problem-for-fano-threefolds-9781009193399","title":"The Calabi Problem for Fano Threefolds","description":"Algebraic 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.\u003cbr\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":50866734792978,"sku":"9781009193399","price":97.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_c018d4db-2768-4d32-9352-aec231823b98.jpg?v=1737694115","url":"https:\/\/surprise-castle.myshopify.com\/products\/the-calabi-problem-for-fano-threefolds-9781009193399","provider":"Surprise Castle","version":"1.0","type":"link"}