Projective duals to algebraic and tropical hypersurfaces. Issue 5 (27th May 2019)

• Record Type: Journal Article
• Authors: Ilten, Nathan; Len, Yoav
• Is Part Of: Proceedings of the London Mathematical Society. Volume 119:Issue 5(2019)
• Page Start: 1234
• Page End: 1278
• Publication Date: 2019-05-27
• Subjects: 14T05 (primary) -- 14N05 (secondary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12268
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: We study a tropical analogue of the projective dual variety of a hypersurface. When X is a curve in P 2 or a surface in P 3, 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 ∗ ) .