English

Stability of tautological bundles on the Hilbert scheme of two points on a surface

Algebraic Geometry 2015-01-14 v3

Abstract

Let (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In this article it is shown that the rank two, respectively rank four tautological sheaf F^{[2]} associated with F on the Hilbert square X^{[2]} is {\mu}-stable with respect to a certain polarization.

Keywords

Cite

@article{arxiv.1202.6528,
  title  = {Stability of tautological bundles on the Hilbert scheme of two points on a surface},
  author = {Malte Wandel},
  journal= {arXiv preprint arXiv:1202.6528},
  year   = {2015}
}

Comments

14 pages, minors corrections of typos, replaced Lemma 2.2 by Def 2.2 and Prop. 2.3, to appear in Nag. Math. J