Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified (Chapman & Hall/CRC Pure and Applied Mathematics Book 273)

differential Forms On Singular Varieties: De Rham And Hodge Theory Simplified Uses Complexes Of Differential Forms To Give A Complete Treatment Of The Deligne Theory Of Mixed Hodge Structures On The Cohomology Of Singular Spaces. This Book Features An Approach That Employs Recursive Arguments On Dimension And Does Not Introduce Spaces Of Higher Dimension Than The Initial Space. It Simplifies The Theory Through Easily Identifiable And Well-defined Weight Filtrations. It Also Avoids Discussion Of Cohomological Descent Theory To Maintain Accessibility. Topics Include Classical Hodge Theory, Differential Forms On Complex Spaces, And Mixed Hodge Structures On Noncompact Spaces. "Differential Forms on Singular Varieties: De Rham and Hodge Theory Simplified uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space. It simplifies the theory through easily identifiable and well-defined weight filtrations, and to maintain accessibility, it also avoids discussion of cohomological descent theory. The treatment is self-contained and brings together information that allows readers to follow and understand this difficult but important subject without jumping from one reference to another."--BOOK JACKET Mathematicians Ancona (U. of Firenze, Italy) and Gaveau (U. of Pierre et Marie Curie, Paris) use complexes of differential forms to provide a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. Their approach employs recursive arguments on dimension, and neither introduces spaces of higher dimens