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出版Cambridge University Press, 2023-06-29
主題Mathematics / Geometry / GeneralMathematics / Topology
ISBN10091933929781009193399
URLhttp://books.google.com.hk/books?id=A-e-EAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.