Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local obstructions to a conformally invariant equation on M\"obius
  surfaces   On a M\"obius surface, as defined by D. Calderbank, we study a variant of the
Einstein-Weyl (EW) equation which we call scalar-flat M\"obius EW (sf-MEW).
This is a conformally invariant, finite type, overdetermined system of
semi-linear partial differential equations. We derive local algebraic
constraints for this equation to admit a solution and give local obstructions.
In the generic case when a certain invariant of the M\"obius structure given by
a symmetric tensor $M_{ab}$ is non-zero, the obstructions are given by
resultants of 3 polynomial equations whose coefficients are conformal
invariants of the M\"obius structure. The vanishing of the resultants is a
necessary condition for there to be solutions to sf-MEW.

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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th