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Mathematics > Algebraic Geometry

arXiv:1807.05416 (math)
[Submitted on 14 Jul 2018 (v1), last revised 19 Aug 2019 (this version, v2)]

Title:On the Gorensteinization of Schubert Varieties via Boundary Divisors

Authors:Sergio Da Silva
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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.
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
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14M15, 13H10
Cite as: arXiv:1807.05416 [math.AG]
  (or arXiv:1807.05416v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.05416

Submission history

From: Sergio Da Silva [view email]
[v1] Sat, 14 Jul 2018 16:19:35 UTC (45 KB)
[v2] Mon, 19 Aug 2019 07:17:42 UTC (69 KB)
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