Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducibility of the intersections of components of a Springer fiber   The description of the intersections of components of a Springer fiber is a
very complex problem. Up to now only two cases have been described completely.
The complete picture for the hook case has been obtained by
  N. Spaltenstein and J.A. Vargas, and for two-row case by
  F.Y.C. Fung. They have shown in particular that the intersection of a pair of
components of a Springer fiber is either irreducible or empty. In both cases
all the components are non-singular and the irreducibility of the intersections
is strongly related to the non-singularity. As it has been shown in [8] a
bijection between orbital varieties and components of the corresponding
Springer fiber in GL_n extends to a bijection between the irreducible
components of the intersections of orbital varieties and the irreducible
components of the intersections of components of Springer fiber preserving
their codimensions. Here we use this bijection to compute the intersections of
the irreducible components of Springer fibers for two-column case. In this case
the components are in general singular. As we show the intersection of two
components is non-empty. The main result of the paper is a necessary and
sufficient condition for the intersection of two components of the Springer
fiber to be irreducible in two-column case. The condition is purely
combinatorial. As an application of this characterization, we give first
examples of pairs of componentswith a reducible intersection having components
of different dimensions.

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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: physics