Duke Mathematical Journal
- Duke Math. J.
- Volume 150, Number 2 (2009), 211-267.
Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles
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
Duke Math. J., Volume 150, Number 2 (2009), 211-267.
First available in Project Euclid: 16 October 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14C05: Parametrization (Chow and Hilbert schemes) 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 18E30: Derived categories, triangulated categories 20C30: Representations of finite symmetric groups
Scala, Luca. Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles. Duke Math. J. 150 (2009), no. 2, 211--267. doi:10.1215/00127094-2009-050. https://projecteuclid.org/euclid.dmj/1255699340