Truncated affine grassmannians and truncated affine Springer fibers for GL₃

2014/01/09 by Zongbin Chen, Chen, Zongbin
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1401.1930

22 pages, 3 tikz pictures

arxiv created 2014/01/09 · arxiv updated 2014/01/10

Abstract

We state a conjecture on how to construct affine pavings for cohomologically pure projective algebraic varieties, which admit an action of torus such that the fixed points and 1-dimensional orbits are finite. Experiments on the affine grassmannian for GL₃ under the guideline of this conjecture, together with the work of Berenstein-Fomin-Zelevinsky and Kamnitzer, have led to the conjecture that the truncated affine grassmannians for GL_r+1 admit affine pavings. For the group GL₃, we construct affine pavings for the truncated affine grassmannians, and we use it to study the affine Springer fibers. In particular, we find a family of truncated affine Springer fibers which are cohomologically pure in the sense of Deligne.

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