Expressive Curves

A real plane algebraic curve C is called expressive if its defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of C. We give a necessary and sufficient criterion for expressivity (subject to a mild technical condition), describe several constructions that produce expressive curves, and relate their study to the combinatorics of plabic graphs, their quivers, and links.

This is joint work with Eugenii Shustin.