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Projective duals to algebraic and tropical hypersurfaces

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

In: Proceedings of the London Mathematical Society, Vol. 119, No. 5, 11.2019, p. 1234-1278.

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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

APA

Ilten, N., & Len, Y. (2019). Projective duals to algebraic and tropical hypersurfaces. Proceedings of the London Mathematical Society, 119(5), 1234-1278. https://doi.org/10.1112/plms.12268

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Ilten N, Len Y. Projective duals to algebraic and tropical hypersurfaces. Proceedings of the London Mathematical Society. 2019 Nov;119(5):1234-1278. https://doi.org/10.1112/plms.12268

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Ilten, Nathan ; Len, Yoav. / Projective duals to algebraic and tropical hypersurfaces. In: Proceedings of the London Mathematical Society. 2019 ; Vol. 119, No. 5. pp. 1234-1278.

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@article{6136c109661344e6ab1021cf7dd6db4d,
title = "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∗).",
author = "Nathan Ilten and Yoav Len",
year = "2019",
month = nov,
doi = "10.1112/plms.12268",
language = "English",
volume = "119",
pages = "1234--1278",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "LONDON MATH SOC",
number = "5",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Projective duals to algebraic and tropical hypersurfaces

AU - Ilten, Nathan

AU - Len, Yoav

PY - 2019/11

Y1 - 2019/11

N2 - 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∗).

AB - 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∗).

U2 - 10.1112/plms.12268

DO - 10.1112/plms.12268

M3 - Article

VL - 119

SP - 1234

EP - 1278

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 5

ER -

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