Real Analytic and Algebraic Singularities

1st Edition

Toshisumi Fukui, Shuichi Izumiya, Satoshi Koike, Toshisumi Fukuda

Chapman and Hall/CRC
Published December 12, 1997
Reference - 232 Pages
ISBN 9780582328747 - CAT# LM2874
Series: Chapman & Hall/CRC Research Notes in Mathematics Series

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Summary

This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

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