  To a braid $\beta\in Br_n$ we associate a complex of sheaves $S_\beta$ on
$Hilb_n(C^2)$ such that the previously defined triply graded link homology of
the closure $L(\beta)$ is isomorphic to the homology of $S_\beta$.
  The construction of $S_\beta$ relies on the Chern functor
  $CH: MF_n^{st}\to D^{per}_{C^*\times C^*}(Hilb_n(C^2))$ defined in the paper
together with its adjoint functor
  $HC$.
  We prove a
  formula for the closure of sufficiently positive elements of the Jucys-Murphy
algebra previously conjectured
  by Gorsky, Negut and Rasmussen.
