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arXiv · 2103.02576

Patchworking the Log-critical locus of planar curves

Lionel Lang·Arthur Renaudineau
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Abstract

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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Lionel Lang, Arthur Renaudineau. 2021-03-03. Patchworking the Log-critical locus of planar curves. https://arxiv.org/abs/2103.02576

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