Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric
  spaces   I use local differential geometric techniques to prove that the algebraic
cycles in certain extremal homology classes in Hermitian symmetric spaces are
either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly
speaking, foliated by rigid subvarieties in a nontrivial way).
  These rigidity results have a number of applications: First, they prove that
many subvarieties in Grassmannians and other Hermitian symmetric spaces cannot
be smoothed (i.e., are not homologous to a smooth subvariety). Second, they
provide characterizations of holomorphic bundles over compact Kahler manifolds
that are generated by their global sections but that have certain polynomials
in their Chern classes vanish (for example, c_2 = 0, c_1c_2 - c_3 = 0, c_3 = 0,
etc.).

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The categories of this paper are: solv-int
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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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
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs