  We will describe a one-step "Gorensteinization" process for a Schubert
variety by blowing-up along its boundary divisor. The local question involves
Kazhdan-Lusztig varieties which can be degenerated to affine toric schemes
defined using the Stanley-Reisner ideal of a subword complex. The blow-up along
the boundary in this toric case is in fact Gorenstein. We show that there
exists a degeneration of the blow-up of the Kazhdan-Lusztig variety to this
Gorenstein scheme, allowing us to extend this result to Schubert varieties in
general. The potential use of this one-step Gorensteinization to describe the
non-Gorenstein locus of Schubert varieties is discussed, as well as the
relationship between Gorensteinizations and the convergence of the Nash blow-up
process in the toric case.
