# Demazure resolutions as varieties of lattices with infinitesimal structure - Mathematics > Algebraic Geometry

Abstract: Let k be a field of positive characteristic. We construct, for each dominantcoweight \lambda of the standard maximal torus in the special linear group, aclosed subvariety D\lambda of the multigraded Hilbert scheme of an affinespace over k, such that the k-valued points of D\lambda can be interpreted aslattices in kz^n endowed with infinitesimal structure. Moreover, for any\lambda we construct a universal homeomorphism from D\lambda to a Demazureresolution of the Schubert variety associated with \lambda in the affineGrassmannian. Lattices in D\lambda have non-trivial infinitesimal structureif and only if they lie over the boundary of the big cell.

Author: Martin Kreidl

Source: https://arxiv.org/