Singularities of Affine Schubert Varieties

J. Kuttler, V. Lakshmibai

Published 2008-09-11, updated 2009-04-18Version 2

This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type $\mathrm{A}^{(1)}_\ell$). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.