Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $O(-2)$ Blow-up Formula via Instanton Calculus on $\hat{C^2/Z_2}$ and
  Weil Conjecture   We calculate Betti numbers of the framed moduli space of instantons on
$\hat{{\bf C}^2/{\bf Z}_2}$, under the assumption that the corresponding
torsion free sheaves $E$ have vanishing properties
($Hom(E,E(-l_\infty))=Ext^2(E,E(-l_\infty))=0$). Moreover we derive the
generating function of Betti numbers and obtain closed formulas. On the other
hand, we derive a universal relation between the generating function of Betti
numbers of the moduli spaces of stable sheaves on $X$ with an $A_1$-singularity
and that on $\hat{X}$ blow-uped at the singularity, by using Weil conjecture.
We call this the $O(-2)$ blow-up formula. Applying this to $X={\bf C}^2/{\bf
Z}_2$ case, we reproduce the formula given by instanton calculus.

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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph