Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gromov-Witten invariants of blow-ups along submanifolds with convex
  normal bundles   Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the
normal bundle of Z in X is convex with a minor assumption, we prove that
genus-zero GW-invariants of Y with cohomology insertions from X, are identical
to GW-invariants of X. Under the same hypothesis, a vanishing theorem is also
proved. An example to which these two theorems apply is when the normal bundle
is generated by global sections. These two main theorems do not hold for
arbitrary blow-ups, and counter-examples are included.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: econ