Complex algebraic threefolds / Masayuki Kawakita.

Format:

Book

Author/Creator:

Kawakita, Masayuki, 1976- author.

Series:

Cambridge studies in advanced mathematics ; 209.

Cambridge studies in advanced mathematics ; 209

Language:

English

Subjects (All):

Threefolds (Algebraic geometry).

Abelian varieties.

Physical Description:

1 online resource (xii, 490 pages) : digital, PDF file(s).

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2024.

Summary:

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.

Contents:

The minimal model program

Singularities

Divisorial contractions to points

Divisorial contractions to curves

Flips

The Sarkisov category

Conical fibrations

Del Pezzo fibrations

Fano threefolds

Minimal models.

Notes:

Title from publisher's bibliographic system (viewed on 29 Sep 2023).

Other Format:

Print version:

ISBN:

9781108933988 (ebook)

Access Restriction:

Restricted for use by site license.