Maximal singular loci of Schubert varieties in SL(n)/B

Details Maximal singular loci of Schubert varieties in SL(n)/B Maximal singular loci of Schubert varieties in SL(n)/B

2001-02-21

arxiv.org/abs/math/0102168v1

Mathematics

Algebraic Geometry

50 pages, 50 figures

Scientific paper

We give an explicit combinatorial description of the irreducible components of the singular locus of the Schubert variety X_w for any element w in S_n. Our description of the irreducible components is computationally more efficient (O(n^6)) than the previously best known algorithms. This result proves a conjecture of Lakshmibai and Sandhya regarding this singular locus. Furthermore, we give simple formulas for calculating the Kazhdan-Lusztig polynomials at the maximum singular points.

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