Multiplicities of Singular Points in Schubert Varieties of Grassmannians
Abstract
We give a closedform formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the identity, and a Grobner basis for the ideal defining the intersection of X with the opposite cell as a closed subvariety of the opposite cell. We give conjectures for the Hilbert function and multiplicity at points other than the identity.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:math/0108071
 Bibcode:
 2001math......8071K
 Keywords:

 Algebraic Geometry;
 14M15
 EPrint:
 11 pages