New derived autoequivalences of Hilbert schemes and generalised Kummer varietiesAndreas Krug
We show that for every smooth projective surface X and every n≥2 the pushforward along the diagonal embedding gives a Pn−1functor into the Snequivariant derived category of X^n. Using the BridgelandKingReidHaiman equivalence this yields a new autoequivalence of the derived category of the Hilbert scheme of n points on X. In the case that the canonical bundle of X is trivial and n=2 this autoequivalence coincides with the known EZspherical twist induced by the boundary of the Hilbert scheme. We also generalise the 16 spherical objects on the Kummer surface given by the exceptional curves to n^4 orthogonal Pn−1Objects on the generalised Kummer variety. Document Actions 
