Projective duals to algebraic and tropical hypersurfaces
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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∗).
Ilten , N & Len , Y 2019 , ' Projective duals to algebraic and tropical hypersurfaces ' , Proceedings of the London Mathematical Society , vol. 119 , no. 5 , pp. 1234-1278 . https://doi.org/10.1112/plms.12268
Proceedings of the London Mathematical Society
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