Variation of mixed Hodge structures and the positivity for algebraic fiber spaces

Details Variation of mixed Hodge structures and the positivity for algebraic fiber spaces Variation of mixed Hodge structures and the positivity for algebraic fiber spaces

2010-08-09

arxiv.org/abs/1008.1489v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing sheaves of Koll\'ar is extended to the sheaves of differential forms of arbitrary degrees in the case of a well prepared birational model. We will also prove the log versions of the results, i.e., the case where we allow horizontal boundary components.

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