Remarks on the derived McKay correspondence for Hilbert schemes of points and tautological bundles

Abstract

We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly from the standard one considerably simplifies both the results and their proofs. As an application, we obtain shorter proofs for known results as well as new formulae for homological invariants of tautological sheaves. In particular, we compute the extension groups between wedge powers of tautological bundles associated to line bundles on the surface.

arXiv commentReferences updated, some typos fixed

References in corpus (9)

• New derived symmetries of some hyperkähler varieties
• Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles
• On equivariant triangulated categories
• Universal Polynomials for Tautological Integrals on Hilbert Schemes
• Derived autoequivalences of generalised Kummer varieties
• Integral Transforms and Deformations of K3 Surfaces
• Geometry and stability of tautological bundles on Hilbert schemes of points
• P-functor versions of the Nakajima operators
• Higher symmetric powers of tautological bundles on Hilbert schemes of points on a surface