Buch, Englisch, Band 485, 455 Seiten, Format (B × H): 230 mm x 151 mm, Gewicht: 664 g
Buch, Englisch, Band 485, 455 Seiten, Format (B × H): 230 mm x 151 mm, Gewicht: 664 g
Reihe: London Mathematical Society Lecture Note Series
ISBN: 978-1-009-19339-9
Verlag: Cambridge University Press
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.
Autoren/Hrsg.
Weitere Infos & Material
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.
