Mathematical Society of Japan Memoirs

Lectures on Complements on Log Surfaces

Yuri G. Prokhorov

Book information

Author
Yuri G. Prokhorov

Publication information
MSJ Memoirs, Volume 10
Tokyo, Japan: The Mathematical Society of Japan, 2001
130 pp.

Dates
Publication date: 2001
First available in Project Euclid: 15 January 2014

Permanent link to this book
https://projecteuclid.org/euclid.msjm/1389800286

Digital Object Identifier:
doi:10.2969/msjmemoirs/010010000

ISBN:
978-4-931469-12-9

Zentralblatt MATH:
1037.14003

Mathematical Reviews (MathSciNet):
MR1830440

Subjects
Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14E5 14J17: Singularities [See also 14B05, 14E15] 14J45: Fano varieties 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
Surfaces, Algebraic

Rights
Copyright © 2001, The Mathematical Society of Japan

Citation
Yuri G. Prokhorov, Lectures on Complements on Log Surfaces (Tokyo: The Mathematical Society of Japan, 2001)

Abstract

Dr. Yuri Prokhorov, the author of this book, is an expert in birational geometry in the field of algebraic geometry. This book is the first significant expository lecture for "complements"; this notion was introduced by Vyacheslav Shokurov quite recently and is important in understanding singularities of a pair consisting of an algebraic variety and a divisor on it. There is currently much ongoing research on this subject, a very active area in algebraic geometry. This book helps the reader to understand the "complement" concept and provides the basic knowledge about the singularities of a pair. The author gives a simple proof of the boundedness of the complements for two dimensional pairs under some restrictive condition, where this boundedness has been conjectured by Shokurov for every dimension. This book contains information and encouragement necessary to attack the problem of the higher dimensional case.