Mixed Hodge Structures and Singularities

Erscheinungsjahr 2012
ISBN: 978-0-521-62060-4
Verlag: Cambridge University Press

Buch, Englisch, Band 132, 208 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 502 g

Reihe: Cambridge Tracts in Mathematics

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.

Autoren/Hrsg.

Kulikov, Valentine S.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

1. Gauss-Manin 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 singularity associated to Brieskorn lattices and mixed Hodge structures.