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

Yujiro Kawamata

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arXiv · 1008.1489

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

Yujiro Kawamata

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Abstract

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 some of the results, i.e., the case where we allow horizontal boundary components.

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Yujiro Kawamata. 2010-08-09. Variation of mixed Hodge structures and the positivity for algebraic fiber spaces. https://arxiv.org/abs/1008.1489

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