Projective duals to algebraic and tropical hypersurfaces
| Autor: | Nathan Ilten, Yoav Len |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics |
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Pure mathematics General Mathematics T-NDAS 0102 computer and information sciences 01 natural sciences Mathematics - Algebraic Geometry Duality (projective geometry) FOS: Mathematics Mathematics - Combinatorics 14T05 14J70 14M99 14N20 QA Mathematics 0101 mathematics Algebraic number QA Algebraic Geometry (math.AG) R2C Mathematics Degree (graph theory) 010102 general mathematics Transformation (function) Hypersurface 010201 computation theory & mathematics Dual polyhedron Combinatorics (math.CO) Variety (universal algebra) BDC |
| Zdroj: | Proceedings of the London Mathematical Society. 119:1234-1278 |
| ISSN: | 1460-244X 0024-6115 |
| DOI: | 10.1112/plms.12268 |
| Popis: | We study a tropical analogue of the projective dual variety of a hypersurface. When $X$ is a curve in $\mathbb{P}^2$ or a surface in $\mathbb{P}^3$, we provide an explicit description of $\text{Trop}(X^*)$ in terms of $\text{Trop}(X)$, as long as $\text{Trop}(X)$ 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 $\text{Trop}(X^*)$. 47 pages, 13 figures; v2 minor revisions; accepted to PLMS |
| Databáze: | OpenAIRE |
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