Injectivity theorems. (English) Zbl 1388.14105

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].


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)