Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Truncated affine grassmannians and truncated affine Springer fibers for
  $\mathrm{GL}_{3}$   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 $\mathrm{GL}_{3}$ 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 $\mathrm{GL}_{r+1}$ admit affine pavings.
  For the group $\mathrm{GL}_{3}$, 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.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph