Stability of tautological bundles on the degree two Hilbert scheme of surfaces

Details Stability of tautological bundles on the degree two Hilbert scheme of surfaces Stability of tautological bundles on the degree two Hilbert scheme of surfaces

2012-02-29

arxiv.org/abs/1202.6528v2

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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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