A Kawamata–Viehweg type formulation of the logarithmic Akizuki–Nakano vanishing theorem

In this article, we present a Kawamata–Viehweg type formulation of the (logarithmic) Akizuki–Nakano Vanishing Theorem. We give two proofs: one by reduction to an older theorem of Steenbrink via Kawamata’s covering lemma, and another by mod p reduction using results of Deligne–Illusie and Hara. We also include two applications.