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.

A detailed treatment of the explicit aspects of the birational geometry of algebraic threefolds arising from the minimal model program.

About the Author
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.

Reviews
'This book is an excellent introduction to the classification of complex algebraic threefolds. It includes a thorough modern treatment and a glimpse into many of the recent higher dimensional breakthroughs.' Christopher Hacon, University of Utah



Book Information
ISBN 9781108844239
Author Masayuki Kawakita
Format Hardback
Page Count 502
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 860g
Dimensions(mm) 236mm * 155mm * 32mm