Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chern Classes of Bundles over Rational Surfaces   Consider the blow up $\pi: \widetilde{X} \to X$ of a rational surface $X$ at
a point. Let $\widetilde{V}$ be a holomorphic bundle over $\widetilde{X}$ whose
restriction to the exceptional divisor equals ${\cal{O}(j) \oplus {\cal O}(-j)$
and define $V =(\pi_*\widetilde{V})^{\vee \vee}.$ Friedman and Morgan gave the
following bounds for the second Chern classes $j \leq c_2(\widetilde{V}) -
c_2(V) \leq j^2.$ We show that these bounds are sharp.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
9
The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph