Extension groups of tautological sheaves on Hilbert schemes

Abstract

We give formulas for the extension groups between tautological sheaves and more general between tautological objects twisted by a determinant line bundle on the Hilbert scheme of points on a smooth quasi-projective surface. We do this using L. Scala's results about the image of tautological sheaves under the Bridgeland-King-Reid equivalence. We also compute the Yoneda products in terms of these formulas.

Revised version

References in corpus (1)

• Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles

Cited by in corpus (3)

• Tautological Sheaves: Stability, Moduli Spaces and Restrictions to Generalised Kummer Varieties
• Tensor products of tautological bundles under the Bridgeland-King-Reid-Haiman equivalence
• On the derived category of the Hilbert scheme of points on an Enriques surface