Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

摘要

We associate to a pair (X,D), consisting of a smooth variety with a divisor D is an element of Div(X) circle times Q whose support has only normal crossings, a canonical Deligne-Mumford stack over X on which D becomes integral. We then reinterpret the Kawamata-Viehweg vanishing theorem as Kodaira vanishing for stacks.