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∗).
Citation
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
Publication
Proceedings of the London Mathematical Society
Status
Peer reviewed
ISSN
0024-6115Type
Journal article
Rights
Copyright © 2019 London Mathematical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1112/plms.12268
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