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Governing singularities of Schubert varieties

Journal of Algebra, 2008
We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, we geometrically prove that this governs (1) the P-locus of a Schubert variety, and (2) which
Alexander Yong
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Normality of Schubert Varieties

American Journal of Mathematics, 1987
Let G be a reductive algebraic group defined over an algebraically closed field. Moreover let Q be a parabolic subgroup. At least three proofs of the normality of the Schubert subvarieties in G/Q are known [\textit{H. H. Andersen}, Invent. Math. 79, 611-618 (1985; Zbl 0591.14036), \textit{S. Ramanan} and \textit{A. Ramanathan}, Invent. Math.
Mehta, V. B., Srinivas, V.
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On Schubert Varieties

Communications in Algebra, 2013
In this article we prove that a Schubert variety X(w) is a toric variety if and only if the Weyl group element w is a product of distinct simple reflections.
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Schubert Varieties and the Variety of Complexes

1983
De Concini and Strickland [s] have obtained interesting results on the “variety of complexes” (e.g. the Cohen-Macaulay nature of its irreducible components) by introducing certain “standard monomials” in its study (see also Kempf [6] for an earlier study of the variety of complexes and [3] for other references).
C. Musili, Conjeeveram S. Seshadri
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Schubert Varieties in the Grassmannian

2016
Throughout our basic goal will be to study Schubert varieties using the standard monomial theory which we shall develop in various situations. This chapter is devoted to the study of Schubert varieties in the Grassmannian, which is a particular case of a more general situation to be treated in the subsequent chapters.
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Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux

Journal of Symbolic Computation, 2021
Oliver Clarke, Fatemeh Mohammadi
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Applications of homogeneous fiber bundles to the Schubert varieties

Geometriae Dedicata, 2023
Mahir Bilen Can
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Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux

Journal of Algebra, 2020
Oliver Clarke, Fatemeh Mohammadi
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Gröbner geometry for skew-symmetric matrix Schubert varieties

Advances in Mathematics, 2022
Eric Marberg, Brendan Pawlowski
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Majority Logic Decoding for Certain Schubert Codes Using Lines in Schubert Varieties

IEEE Transactions on Information Theory, 2022
Prasant Singh
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