On Multiplicities of Points on Schubert Varieties in Graßmannians II
نویسنده
چکیده
We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graßmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is accomplished by relating these sets of reflections to the author’s previous combinatorial interpretation of these multiplicities in terms of non-intersecting lattice paths (Séminaire Lotharingien Combin. 45 (2001), Article B45c). Moreover, we provide a compact formula for the Hilbert series of the tangent cone to a Schubert variety in a Graßmannian assuming the truth of another conjecture of Kreiman and Lakshmibai.
منابع مشابه
Multiplicities of Points on Schubert Varieties in Grassmannians
An important invariant of a singular point on an algebraic variety X is its multiplicity : the normalized leading coefficient of the Hilbert polynomial of the local ring. The main result of the present note is an explicit determinantal formula for the multiplicities of points on Schubert varieties in Grassmannians. This is a simplification of a formula obtained in [5]. More recently, the recurr...
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