Expressive curves

Abstract: The talk is devoted to a class of real plane algebraic curves which we call expressive. These are the curves whose defining polynomial has the smallest number of critical points allowed by the topology of the real point set. This concept can be viewed as a global version of the notion of a real morsification of an isolated real plane curve singularity. We provide a characterization of expressive curves and describe several constructions that produce a large number of example of expressive curves. Finally, we discuss further potential developments towards combinatorics of divides, topology of links at infinity, mutations of quivers etc. Joint work with Sergey Fomin.

algebraic geometrycombinatorics

Audience: researchers in the topic

( paper )

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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