Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

Kenji Matsuki; Martin Olsson

Kawamata-Viehweg vanishing as Kodaira vanishing for stacks

Algebraic Geometry 2007-05-23 v1

Authors: Kenji Matsuki , Martin Olsson

Abstract

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.

Keywords

kawamata-viehweg vanishing kodaira vanishing deligne-mumford stack normal crossings divisor pair

Cite

@article{arxiv.math/0212259,
  title  = {Kawamata-Viehweg vanishing as Kodaira vanishing for stacks},
  author = {Kenji Matsuki and Martin Olsson},
  journal= {arXiv preprint arXiv:math/0212259},
  year   = {2007}
}

Comments

9 pages

Related papers

View all related →