Mathematical Society of Japan Memoirs

Lectures on Complements on Log Surfaces

Yuri G. Prokhorov

Book information

Yuri G. Prokhorov

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

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

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Zentralblatt MATH:

Mathematical Reviews (MathSciNet):

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

Copyright © 2001, The Mathematical Society of Japan

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


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.