Injectivity theorems. (English) Zbl 1388.14105

Fujino, Osamu

Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 131-157 (2017).

Summary: We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional algebraic varieties. We also treat some applications.
For the entire collection see [Zbl 1388.14012].

MSC:

14J10	Families, moduli, classification: algebraic theory
14D07	Variation of Hodge structures (algebro-geometric aspects)
14F17	Vanishing theorems in algebraic geometry
14E30	Minimal model program (Mori theory, extremal rays)

Keywords:

mixed Hodge structures on cohomology with compact support; Du Bois singularities; Du Bois complexes; injectivity theorems; simple normal crossing varieties; extension theorems