Mixed Hodge Structures and Singularities [Hardcover]

This 1998 book is a modern introduction to, and a survey of, some topics of singularity theory.This book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying singularities by means of differential forms. Using the language of algebraic geometry, the author strikes a balance between the traditional approach to the subject, and the more abstract homologic al approach.This will be an excellent resource for all researchers whose interests lie in singularity theory, algebraic or differential geometry.This book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying singularities by means of differential forms. Using the language of algebraic geometry, the author strikes a balance between the traditional approach to the subject, and the more abstract homologic al approach.This will be an excellent resource for all researchers whose interests lie in singularity theory, algebraic or differential geometry.This vital work is both an introduction to, and a survey of singularity theory, in particular, studying 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 is an excellent resource for all researchers in singularity theory, algebraic or differential geometry.1. GaussManin connection; 2. Limit mixed Hodge structure on the vanishing cohomology of an isolated hypersurface singularity; 3. The period map of a m-constant deformation of an isolated hypersurface singlƒ«