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Variation of mixed Hodge structures and the positivity for algebraic fiber spaces. (English) Zbl 1360.14034
Chen, Jungkai Alfred (ed.) et al., Algebraic geometry in East Asia – Taipei 2011. Proceedings of the conference, Taipei, Taiwan, November 16–20, 2011. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-024-2). Advanced Studies in Pure Mathematics 65, 27-57 (2015).
Summary: 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 Kollár 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.
For the entire collection see [Zbl 1321.14003].

MSC:
14D07 Variation of Hodge structures (algebro-geometric aspects)
14D06 Fibrations, degenerations in algebraic geometry
32G20 Period matrices, variation of Hodge structure; degenerations
14E30 Minimal model program (Mori theory, extremal rays)
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