Projective duals to algebraic and tropical hypersurfaces. Issue 5 (27th May 2019) - Ilten, Nathan; Len, Yoav
Abstract: We study a tropical analogue of the projective dual variety of a hypersurface. When X is a curve in P 2 or a surface in P 3, 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 ∗ ) .