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Hodge theory

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Hodge theory --- Geometry, Algebraic

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This 1998 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.

Hodge theory. --- Singularities (Mathematics)

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Hodge theory. --- Homology theory. --- Théorie de Hodge --- Homologie --- Hodge theory --- Homology theory --- Théorie de Hodge

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"We use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal. We analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements"--

Geometry, Algebraic. --- Hodge theory. --- Surfaces, Algebraic. --- Géométrie algébrique. --- Hodge, Théorie de. --- Surfaces algébriques. --- Hodge theory --- Geometry, Algebraic