The Calabi problem for Fano threefolds
著者
書誌事項
The Calabi problem for Fano threefolds
（London Mathematical Society lecture note series, 485）
Cambridge University Press, 2023
- : pbk
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注記
Other authors: Ana-Maria Castravet, Ivan Cheltsov, Kento Fujita, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Süß, Nivedita Viswanathan
Includes bibliographical references (p. 430-439) and index
内容説明・目次
内容説明
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 Kahler-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 Kahler-Einstein metric, containing many additional relevant results such as the classification of all Kahler-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.
目次
- Introduction
- 1. K-stability
- 2. Warm-up: smooth del Pezzo surfaces
- 3. Proof of main theorem: known cases
- 4. Proof of main theorem: special cases
- 5. Proof of main theorem: remaining cases
- 6. The big table
- 7. Conclusion
- Appendix. Technical results used in proof of main theorem
- References
- Index.
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