English

Restriction theorems for $\mu$-(semi)stable framed sheaves

Algebraic Geometry 2013-11-14 v3

Abstract

We provide a generalization of Mehta-Ramanathan theorems to framed sheaves: we prove that the restriction of a μ\mu-semistable framed sheaf on a nonsingular projective irreducible variety, of dimension greater or equal than two, to a general hypersurface of sufficiently high degree is again μ\mu-semistable. The same holds for μ\mu-stability under some additional assumptions.

Keywords

Cite

@article{arxiv.1010.5096,
  title  = {Restriction theorems for $\mu$-(semi)stable framed sheaves},
  author = {Francesco Sala},
  journal= {arXiv preprint arXiv:1010.5096},
  year   = {2013}
}

Comments

v2: incorporates changes suggested by the referee. v3: some intermediate results on the (relative) Harder-Narasimhan filtration and the Jordan-Holder filtrations have been extended to the case of framed sheaves on schemes. The main results are unchanged. To appear in Journal of Pure and Applied Algebra

R2 v1 2026-06-21T16:33:38.578Z