Abstract
We study tautological sheaves on the Hilbert scheme of points on a smooth quasi-projective algebraic surface by means of the Bridgeland–King–Reid transform. We obtain Brion–Danila’s Formulas for the derived direct image of tautological sheaves or their double tensor product for the Hilbert–Chow morphism; as an application we compute the cohomology of the Hilbert scheme with values in tautological sheaves or in their double tensor product, thus generalizing results previously obtained for tautological bundles.
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Scala, L. Some remarks on tautological sheaves on Hilbert schemes of points on a surface. Geom Dedicata 139, 313–329 (2009). https://doi.org/10.1007/s10711-008-9338-x
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DOI: https://doi.org/10.1007/s10711-008-9338-x