On the Gorensteinization of Schubert Varieties via Boundary Divisors
Abstract
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.
Keywords
Cite
@article{arxiv.1807.05416,
title = {On the Gorensteinization of Schubert Varieties via Boundary Divisors},
author = {Sergio Da Silva},
journal= {arXiv preprint arXiv:1807.05416},
year = {2019}
}
Comments
40 pages, 8 figures, shortened version of PhD thesis. The second version contains important new results, including a combinatorial description for the exceptional divisors in the degeneration as well as a subword description for non-Gorenstein Kazhdan-Lusztig varieties. These results can be found in Section 2.3