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Mixed Hodge Structures and Singularities : Cambridge Tracts in Mathematics - Valentine S. Kulikov

Mixed Hodge Structures and Singularities

Cambridge Tracts in Mathematics


Published: 20th January 2012
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This book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms. Here some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss-Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This will be an excellent resource for all researchers whose interests lie in singularity theory, and algebraic or differential geometry.

'Without any doubt, the author has covered a wealth of material on a highly advanced topic in complex geometry, and in this regard he has provided a great service to the mathematical community ... he has succeeded in providing a brilliant introduction to, and a comprehensive overview of, this contemporary central subject of complex geometry ... the entire text represents an irresistible invitation to the subject, and may be seen as a dependable pathfinder with regard to the vast existing original literature in the field.' W. Kleinert, Zentralblatt fur Mathematik und ihre Grenzgebiete

GaussâÇôManin connection
Limit mixed Hodge structure on the vanishing cohomology of an isolated hypersurface singularity
The period map of a m-constant deformation of an isolated hypersurface singularity associated to Brieskorn lattices and mixed Hodge structures
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521620604
ISBN-10: 0521620600
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 212
Published: 20th January 2012
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.6
Weight (kg): 0.48