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arXiv · 1202.6528

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

Malte Wandel
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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.

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Malte Wandel. 2012-02-29. Stability of tautological bundles on the Hilbert scheme of two points on a surface. https://doi.org/10.1215/00277630-2416410

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