Complex Algebraic Threefolds

Erscheinungsjahr 2023
ISBN: 978-1-108-84423-9
Verlag: Cambridge University Press

Buch, Englisch, Band 209, 502 Seiten, Format (B × H): 152 mm x 230 mm, Gewicht: 907 g

Reihe: Cambridge Studies in Advanced Mathematics

The first book on the explicit birational geometry of complex algebraic threefolds arising from the minimal model program, this text is sure to become an essential reference in the field of birational geometry. Threefolds remain the interface between low and high-dimensional settings and a good understanding of them is necessary in this actively evolving area. Intended for advanced graduate students as well as researchers working in birational geometry, the book is as self-contained as possible. Detailed proofs are given throughout and more than 100 examples help to deepen understanding of birational geometry. The first part of the book deals with threefold singularities, divisorial contractions and flips. After a thorough explanation of the Sarkisov program, the second part is devoted to the analysis of outputs, specifically minimal models and Mori fibre spaces. The latter are divided into conical fibrations, del Pezzo fibrations and Fano threefolds according to the relative dimension.

Autoren/Hrsg.

Kawakita, Masayuki

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

1. The minimal model program; 2. Singularities; 3. Divisorial contractions to points; 4. Divisorial contractions to curves; 5. Flips; 6. The Sarkisov category; 7. Conical fibrations; 8. Del Pezzo fibrations; 9. Fano threefolds; 10. Minimal models; References; Notation; Index.

Über Autor(innen)

Kawakita, Masayuki
Masayuki Kawakita is Associate Professor at the Research Institute for Mathematical Sciences, Kyoto University. He has established a classification of threefold divisorial contractions and is a leading expert in algebraic threefolds.