Projective duals to algebraic and tropical hypersurfaces

Nathan Ilten, Yoav Len

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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).
Original languageEnglish
Pages (from-to)1234-1278
JournalProceedings of the London Mathematical Society
Volume119
Issue number5
Early online date27 May 2019
DOIs
Publication statusPublished - Nov 2019

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