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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 Khler-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 Khler-Einstein metric, containing many additional relevant results such as the classification of all Khler-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.
- Illustratör: Worked examples or Exercises
- Format: Pocket/Paperback
- ISBN: 9781009193399
- Språk: Engelska
- Antal sidor: 455
- Utgivningsdatum: 2023-06-29
- Förlag: Cambridge University Press