The geometry of the flex locus of a hypersurface

We give a formula in terms of multidimensional resultants for an equation for the flex locus of a projective hypersurface, generalizing a classical result of Salmon for surfaces. Using this formula, we compute the dimension of this flex locus, and an upper bound for the degree of its defining equati...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Authors: Busé, Laurent, D'Andrea, Carlos, Sombra, Martin, Weimann, Martin
Format: Article
Language:English
Subjects:
Formulas (mathematics)
Hyperspaces
Loci
Resultants
Upper bounds
Online Access:Get full text
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Summary:We give a formula in terms of multidimensional resultants for an equation for the flex locus of a projective hypersurface, generalizing a classical result of Salmon for surfaces. Using this formula, we compute the dimension of this flex locus, and an upper bound for the degree of its defining equations. We also show that, when the hypersurface is generic, this bound is reached, and that the generic flex line is unique and has the expected order of contact with the hypersurface.
ISSN:2331-8422
DOI:10.48550/arxiv.1804.08025