P-functor versions of the Nakajima operators

Abstract

For every smooth quasi-projective surface X we construct a series of P^{n-1}-functors H_{l,n}: D(X x X^[l]) --> D(X^[n+l]) between the derived categories of the Hilbert schemes of points for n>max{l,1} using the derived McKay correspondence. They can be considered as analogues of the Nakajima operators. The functors also restrict to P^{n-1}-functors on the generalised Kummer varieties. We also study the induced autoequivalences and obtain, for example, a universal braid relation in the groups of derived autoequivalences of Hilbert squares of K3 surfaces and Kummer fourfolds.

References in corpus (7)

• 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
• On adjunctions for Fourier-Mukai transforms
• Categories of Massless D-Branes and del Pezzo Surfaces
• Derived autoequivalences of generalised Kummer varieties
• Spherical functors on the Kummer surface

Cited by in corpus (7)

• Equivalences of equivariant derived categories
• Derived categories of (nested) Hilbert schemes
• Mukai flops and P-twists
• ${\mathbb{P}}^n$-functors
• Universal functors on symmetric quotient stacks of Abelian varieties
• Remarks on the derived McKay correspondence for Hilbert schemes of points and tautological bundles
• Hochschild cohomology and deformations of $\mathbb{P}$-functors