Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some characterizations of singular components of Springer fibers in the
  two-column case   Let $u$ be a nilpotent endomorphism of a finite dimensional
$\mathbb{C}$-vector space. The set ${\mathcal F}_u$ of $u$-stable complete
flags is a projective algebraic variety called a Springer fiber. Its
irreducible components are parameterized by a set of standard tableaux. We
provide three characterizations of the singular components of ${\mathcal F}_u$
in the case $u^2=0$. First, we give the combinatorial description of standard
tableaux corresponding to singular components. Second, we prove that a
component is singular if and only if its Poincar\'e polynomial is not
palindromic. Third, we show that a component is singular when it has too many
intersections of codimension one with other components. Finally, relying on the
second criterion, we infer that, for $u$ general, whenever ${\mathcal F}_u$ has
a singular component, it admits a component whose Poincar\'e polynomial is not
palindromic. This work relies on a previous criterion of singularity for
components of ${\mathcal F}_u$ in the case $u^2=0$ by the first author and on
the description of the $B$-orbit decomposition of orbital varieties of
nilpotent order two by the second author.

3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int