Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kodaira Dimension and the Yamabe Problem   The Yamabe invariant Y(M) of a smooth compact manifold is roughly the
supremum of the scalar curvatures of unit-volume constant-scalar curvature
Riemannian metrics g on M. (To be absolutely precise, one only considers
constant-scalar-curvature metrics which are Yamabe minimizers, but this does
not affect the sign of the answer.) If M is the underlying smooth 4-manifold of
a complex algebraic surface (M,J), it is shown that the sign of Y(M) is
completely determined by the Kodaira dimension Kod (M,J). More precisely, Y(M)
< 0 iff Kod (M,J)=2; Y(M) = 0 iff Kod (M,J)=0 or 1; and Y(M) > 0 iff Kod (M,J)=
-infinity.

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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics