This is the first comprehensive basic monograph on mixed Hodge
structures. Starting with a summary of classic Hodge theory from a
modern vantage point the book goes on to explain Deligne's mixed
Hodge theory. Here proofs are given using cubical schemes rather
than simplicial schemes. Next come Hain's and Morgan's results on
mixed Hodge structures related to homotopy theory. Steenbrink's
approach of the limit mixed Hodge structure is then explained using
the language of nearby and vanishing cycle functors bridging the
passage to Saito's theory of mixed Hodge modules which is the
subject of the last chapter. Since here D-modules are essential,
these are briefly introduced in a previous chapter. At various
stages applications are given, ranging from the Hodge conjecture to
singularities. The book ends with three large appendices, each one
in itself a resourceful summary of tools and results not easily
found in one place in the existing literature (homological algebra,
algebraic and differential topology, stratified spaces and
singularities). The book is intended for advanced graduate
students, researchers in complex algebraic geometry as well as
interested researchers in nearby fields (algebraic geometry,
mathematical physics
General
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