arXiv Analytics

Sign in

arXiv:math/0411127 [math.AG]AbstractReferencesReviewsResources

On Ideal Generators for Affine Schubert Varieties

V. Kreiman, V. Lakshmibai, P. Magyar, J. Weyman

Published 2004-11-06Version 1

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by restricting certain Pl\"ucker co-ordinates. As a consequence, we write an explicit set of generators for the degree-one part of the ideal of the finite-dimensional embedding. This in turn gives a set of generators for the degree-one part of the ideal defining the affine Grassmannian inside the infinite Grassmannian which we conjecture to be a complete set of ideal generators. We apply our results to the orbit closures of nilpotent matrices. We describe (in a characteristic-free way) a filtration for the coordinate ring of a nilpotent orbit closure and state a conjecture on the SL(n)-module structures of the constituents of this filtration.

Related articles: Most relevant | Search more
arXiv:math/0603273 [math.AG] (Published 2006-03-12, updated 2006-06-29)
Governing Singularities of Schubert Varieties
arXiv:1701.05956 [math.AG] (Published 2017-01-21)
Cominuscule points and Schubert varieties
arXiv:1106.2586 [math.AG] (Published 2011-06-14, updated 2015-02-07)
Projected Richardson varieties and affine Schubert varieties