Georgia Institute of Technology College of Sciences

Motivated by applications and the classical theory of A-discriminants of Gel'fand, Kapranov, and Zelevinsky, we develop the basic theory of discriminants of multivariate reciprocal polynomials. These reciprocal discriminants parameterize reciprocal polynomials that define a singular hypersurface. We show that a reciprocal discriminant has a rich combinatorial structure. It is a reducible hypersurface whose components are dual varieties to Chebyshev subvarieties which correspond to certain layers in a toric arrangement associated to the exponents of the reciprocal polynomials. The layers which contribute correspond to certain matroidal decompositions of the exponents.

This is joint work with Trevor Karn and Simon Telen.