Patchworking the Log-critical locus of planar curves

Abstract: We will report on a recent work in collaboration with A. Renaudineau in which we studied the critical locus for the amoeba map along families of curves defined by Viro polynomials. Recall that for real curves, this locus is a superset of the real part. In general, this locus gives informations on how the curve sits in the plane. Unfortunately, not much is known on its topology besides some bounds on its Betti numbers. We will see that the Log-critical locus admits a Patchworking theorem. We will discuss some constructions and address the sharpness of the bounds mentioned above.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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