English

Ample tangent bundle on smooth projective stacks

Algebraic Geometry 2016-11-08 v1

Abstract

We study ample vector bundles on smooth projective stacks. In particular, we prove that the tangent bundle for the weighted projective stack P(a0,...,an)\mathbb{P}(a_0,...,a_n) is ample. A result of Mori shows that the only smooth projective varieties with ample vector bundle are isomorphic to PN\mathbb{P}^N for some NN. Extending our geometric spaces from varieties to projective stacks, we are able to provide a new example. This leaves the open question of knowing if the only smooth projective stacks are the weighted projective stacks.

Keywords

Cite

@article{arxiv.1611.01809,
  title  = {Ample tangent bundle on smooth projective stacks},
  author = {Karim El Haloui},
  journal= {arXiv preprint arXiv:1611.01809},
  year   = {2016}
}

Comments

13 pages

R2 v1 2026-06-22T16:43:30.754Z