Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their
  blowups   Shortly after the introduction of Seiberg-Witten theory, LeBrun showed that
the sign of the Yamabe invariant of a compact K\"ahler surface is determined by
its Kodaira dimension. In this paper, we show that LeBrun's Theorem is no
longer true for non-K\"ahler surfaces. In particular, we show that the Yamabe
invariants of Inoue surfaces and their blowups are all zero. We also take this
opportunity to record a proof that the Yamabe invariants of Kodaira surfaces
and their blowups are all zero, as previously indicated by LeBrun.

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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org