Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

Details Kawamata-Viehweg vanishing as Kodaira vanishing for stacks Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

2002-12-19

arxiv.org/abs/math/0212259v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

We associate to a pair $(X,D)$, consisting of a smooth scheme with a divisor
$D\in \text{Div}(X)\otimes \mathbb{Q}$ whose support is a divisor with 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.

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