Projective duals to algebraic and tropical hypersurfaces
Nathan Ilten, Yoav Len

TL;DR
This paper explores the tropical analogue of projective duality for hypersurfaces, providing explicit descriptions for curves and surfaces under certain conditions, and extending classical duality results to tropical geometry.
Contribution
It introduces a tropical dual variety concept, explicitly describes it for curves and surfaces, and connects tropical duality with classical geometric formulas.
Findings
Explicit description of Trop(X*) for curves and surfaces
Transformation of Newton polygons under duality
Extension of classical duality formulas to tropical setting
Abstract
We study a tropical analogue of the projective dual variety of a hypersurface. When is a curve in or a surface in , we provide an explicit description of in terms of , as long as is smooth and satisfies a mild genericity condition. As a consequence, when 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 , we give a partial description of .
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