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Working paper

Hilbert schemes and y-ification of Khovanov-Rozansky homology

Gorsky E., Hogancamp M.
We define a deformation of the triply graded Khovanov-Rozansky homology of a link L depending on a choice of parameters for each component of L.  We conjecture that this invariant restores the missing symmetry of the triply graded Khovanov-Rozansky homology, and in addition satisfies a number of predictions coming from a conjectural connection with Hilbert schemes of points in the plane. We compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme. symmetry of the triply graded Khovanov-Rozansky homology, and in addition satisfies a number of predictions coming from a conjectural connection with Hilbert schemes of points in the plane. We compute this invariant for all positive powers of the full twist and match it to the family of ideals appearing in Haiman's description of the isospectral Hilbert scheme.