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- W2950376105 abstract "We study Hilbert-Samuel multiplicity for points of Schubert varieties in the complete flag variety, by Groebner degenerations of the Kazhdan-Lusztig ideal. In the covexillary case, we give a positive combinatorial rule for multiplicity by establishing (with a Groebner basis) a reduced and equidimensional limit whose Stanley-Reisner simplicial complex is homeomorphic to a shellable ball or sphere. We show that multiplicity counts the number of facets of this complex. We also obtain a formula for the Hilbert series of the local ring. In particular, our work gives a multiplicity rule for Grassmannian Schubert varieties, providing alternative statements and proofs to formulae of [Lakshmibai-Weyman '90], [Rosenthal-Zelevinsky '01], [Krattenthaler '01], [Kreiman-Lakshmibai '04] and [Woo-Yong '09]. We suggest extensions of our methodology to the general case." @default.
- W2950376105 created "2019-06-27" @default.
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- W2950376105 date "2010-01-19" @default.
- W2950376105 modified "2023-09-25" @default.
- W2950376105 title "Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties" @default.
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- W2950376105 doi "https://doi.org/10.48550/arxiv.1001.3437" @default.
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