Projective duals to algebraic and tropical hypersurfaces

Nathan Ilten; Yoav Len

doi:10.1112/plms.12268

Projective duals to algebraic and tropical hypersurfaces

Nathan Ilten, Yoav Len

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1234-1278
Journal	Proceedings of the London Mathematical Society
Volume	119
Issue number	5
Early online date	27 May 2019
DOIs	https://doi.org/10.1112/plms.12268
Publication status	Published - Nov 2019

Access to Document

10.1112/plms.12268

Ilten Len PLMS accepted
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
Accepted author manuscript, 509 KB

Yoav Len
- yoav.lenst-andrews.acuk
- Pure Mathematics - Lecturer in Pure Mathematics
Person: Academic

Cite this

@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",

}

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

SN - 0024-6115

VL - 119

SP - 1234

EP - 1278

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 5

ER -

Projective duals to algebraic and tropical hypersurfaces

Abstract

Access to Document

Fingerprint

Profiles

Yoav Len

Cite this