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...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2103.02576 |