Abstract
Let be the Hilbert scheme of points on the smooth quasi-projective surface , and let be the tautological bundle on naturally associated to the line bundle on . As a corollary of Haiman's results, we express the image of the tautological bundle for the Bridgeland-King-Reid equivalence in terms of a complex of -equivariant sheaves in and we characterize the image in terms of the hyperderived spectral sequence associated to the derived -fold tensor power of the complex . The study of the -invariants of this spectral sequence allows us to get the derived direct images of the double tensor power and of the general -fold exterior power of the tautological bundle for the Hilbert-Chow morphism, providing Danila-Brion-type formulas in these two cases. This easily yields the computation of the cohomology of with values in and
Citation
Luca Scala. "Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles." Duke Math. J. 150 (2) 211 - 267, 1 November 2009. https://doi.org/10.1215/00127094-2009-050
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