English

Fibr\'es paraboliques et champ des racines

Algebraic Geometry 2007-05-23 v1

Abstract

Following ideas of Nori, Biswas, ..., we show that given an integer r>0, a noetherian scheme X, and an effective Cartier divisor D on it, the parabolic vector bundles on (X,D) with weights multiples of 1/r (in the sense of Maruyama-Yokogawa) are equivalent to ordinary vector bundles on an orbifold, the stack of r-th roots associated to (X,D) (a twisted scheme in the sense of Abramovich-Vistoli). We use this fact to get some information on the finite parabolic bundles on the (pointed) projective line.

Keywords

Cite

@article{arxiv.math/0604458,
  title  = {Fibr\'es paraboliques et champ des racines},
  author = {Niels Borne},
  journal= {arXiv preprint arXiv:math/0604458},
  year   = {2007}
}

Comments

32 pages

R2 v1 2026-07-22T17:34:47.977Z