English

Connections for weighted projective lines

Algebraic Geometry 2009-04-23 v1

Abstract

We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Huebner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves equipped with such a connection, and one passes to the perpendicular category to a nonzero vector bundle without self-extensions, then the resulting category is equivalent to the category of representations of a deformed preprojective algebra.

Keywords

Cite

@article{arxiv.0904.3430,
  title  = {Connections for weighted projective lines},
  author = {William Crawley-Boevey},
  journal= {arXiv preprint arXiv:0904.3430},
  year   = {2009}
}

Comments

12 pages

R2 v1 2026-06-21T12:53:56.189Z