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Mixed Hodge Structures [electronic resource] /by Chris A.M. Peters, Joseph H.M. Steenbrink.

by Peters, Chris A.M [author.]; Steenbrink, Joseph H.M [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics: 52Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.Description: XIV, 470 p. online resource.ISBN: 9783540770176.Subject(s): Mathematics | Geometry, algebraic | Global differential geometry | Topology | Mathematical physics | Mathematics | Algebraic Geometry | Differential Geometry | Topology | Mathematical Methods in PhysicsDDC classification: 516.35 Online resources: Click here to access online
Contents:
Basic Hodge Theory -- Compact Kähler Manifolds -- Pure Hodge Structures -- Abstract Aspects of Mixed Hodge Structures -- Mixed Hodge Structures on Cohomology Groups -- Smooth Varieties -- Singular Varieties -- Singular Varieties: Complementary Results -- Applications to Algebraic Cycles and to Singularities -- Mixed Hodge Structures on Homotopy Groups -- Hodge Theory and Iterated Integrals -- Hodge Theory and Minimal Models -- Hodge Structures and Local Systems -- Variations of Hodge Structure -- Degenerations of Hodge Structures -- Applications of Asymptotic Hodge Theory -- Perverse Sheaves and D-Modules -- Mixed Hodge Modules.
In: Springer eBooksSummary: This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed and exhaustive fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory: variations of Hodge structures, the limit mixed Hodge structure, and then, in the final chapter the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.
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Basic Hodge Theory -- Compact Kähler Manifolds -- Pure Hodge Structures -- Abstract Aspects of Mixed Hodge Structures -- Mixed Hodge Structures on Cohomology Groups -- Smooth Varieties -- Singular Varieties -- Singular Varieties: Complementary Results -- Applications to Algebraic Cycles and to Singularities -- Mixed Hodge Structures on Homotopy Groups -- Hodge Theory and Iterated Integrals -- Hodge Theory and Minimal Models -- Hodge Structures and Local Systems -- Variations of Hodge Structure -- Degenerations of Hodge Structures -- Applications of Asymptotic Hodge Theory -- Perverse Sheaves and D-Modules -- Mixed Hodge Modules.

This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed and exhaustive fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory: variations of Hodge structures, the limit mixed Hodge structure, and then, in the final chapter the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.

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