Projective duals to algebraic and tropical hypersurfaces

Abstract

We study a tropical analogue of the projective dual variety of a hypersurface. When X is a curve in ℙ2 or a surface in ℙ3, we provide an explicit description of Trop(X∗) in terms of Trop(X), as long as Trop(X) is smooth and satisfies a mild genericity condition. As a consequence, when X is a curve we describe the transformation of Newton polygons under projective duality, and recover classical formulas for the degree of a dual plane curve. For higher dimensional hypersurfaces X, we give a partial description of Trop(X∗).