Demazure resolutions as varieties of lattices with infinitesimal structure

Details Demazure resolutions as varieties of lattices with infinitesimal structure Demazure resolutions as varieties of lattices with infinitesimal structure

2009-07-22

arxiv.org/abs/0907.3855v2

J. Algebra 324, 2010, pp. 541--564

Mathematics

Algebraic Geometry

24 pages, added the missing bibliography

Scientific paper

Let k be a field of positive characteristic. We construct, for each dominant coweight \lambda of the standard maximal torus in the special linear group, a closed subvariety D(\lambda) of the multigraded Hilbert scheme of an affine space over k, such that the k-valued points of D(\lambda) can be interpreted as lattices in k((z))^n endowed with infinitesimal structure. Moreover, for any \lambda we construct a universal homeomorphism from D(\lambda) to a Demazure resolution of the Schubert variety associated with \lambda in the affine Grassmannian. Lattices in D(\lambda) have non-trivial infinitesimal structure if and only if they lie over the boundary of the big cell.

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