Michigan Math. J. 71 (2), 373-399, (May 2022) DOI: 10.1307/mmj/20195812
KEYWORDS: 14F17, 14F10, 14D07
We prove an injectivity and vanishing theorem for Hodge modules and -divisors over projective varieties, extending the results for rational Hodge modules and integral divisors in [Wu17]. In particular, the injectivity generalizes the fundamental injectivity of Esnault–Viehweg for normal crossing -divisors, whereas the vanishing generalizes Kawamata–Viehweg vanishing for -divisors. As a main application, we also deduce a Fujita-type freeness result for Hodge modules in the normal crossing case.