Calabi Problem for Fano Threefolds
Carolina Araujo
Bok Engelsk 2023 · Llibres electrònics
| Medvirkende | Castravet, Ana-Maria, (author.)
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| Utgitt | Cambridge University Press , 2023
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| Omfang | ill
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| Utgave | 1st ed.
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| Opplysninger | 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.
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| Dewey | |
| ISBN | 9781009193382
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