English

A stacky approach to identifying the semistable locus of bundles

Algebraic Geometry 2025-03-18 v3

Abstract

We show that the semistable locus is the unique maximal open substack of the moduli stack of principal bundles over a curve that admits a schematic moduli space. For rank 22 vector bundles it coincides with the unique maximal open substack that admits a separated moduli space, but for higher rank there exist other open substacks that admit separated moduli spaces.

Keywords

Cite

@article{arxiv.2302.09245,
  title  = {A stacky approach to identifying the semistable locus of bundles},
  author = {Dario Weissmann and Xucheng Zhang},
  journal= {arXiv preprint arXiv:2302.09245},
  year   = {2025}
}

Comments

Theorem A now includes the case of semistable principal bundles and the characteristic can be arbitrary in Theorem B and C. To appear in Algebraic Geometry (AG)