Da Silva, Sergio Mathew Luis2018-10-232018-10-232018-05-30DaSilva_cornellgrad_0058F_10881http://dissertations.umi.com/cornellgrad:10881bibid: 10489576https://hdl.handle.net/1813/59491We 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.en-USAlgebraic GeometryMathematicstoric varietyGorenstein VarietyKazhdan-Lusztig VarietySchubert Varietydissertation or thesishttps://doi.org/10.7298/X4RB72V7