Skip to main content
eScholarship
Open Access Publications from the University of California

UC Davis

UC Davis Previously Published Works bannerUC Davis

Hilbert schemes and y–ification of Khovanov–Rozansky homology

Abstract

We define a deformation of the triply graded Khovanov–Rozansky homology of a link L depending on a choice of parameters yc for each component of L, which satisfies link-splitting properties similar to the Batson–Seed invariant. Keeping the yc as formal variables yields a link homology valued in triply graded modules over ℚ[xc, yc]c∈π0(L). We conjecture that this invariant restores the missing Q ↔ T Q-1 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 schem

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View