Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Patchworking the Log-critical locus of planar curves   We establish a patchworking theorem \`a la Viro for the Log-critical locus of
algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the
existence of projective curves of arbitrary degree with smooth connected
Log-critical locus. To prove our patchworking theorem, we study the behaviour
of Log-inflection points along families of curves defined by Viro polynomials.
In particular, we prove a generalisation of a theorem of Mikhalkin and the
second author on the tropical limit of Log-inflection points.

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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an