Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of holomorphic sections and perturbation of positive line
  bundles over $q$--concave manifolds   By using asymptotic Morse inequalities we give a lower bound for the space of
holomorphic sections of high tensor powers in a positive line bundle over a
q-concave domain. The curvature of the positive bundle induces a hermitian
metric on the manifold. The bound is given explicitely in terms of the volume
of the domain in this metric and a certain integral on the boundary involving
the defining function and its Levi form. As application we study the
perturbattion of the complex structure of a q-concave manifold.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom