Vol. 304, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
The geometry of the flex locus of a hypersurface

Laurent Busé, Carlos D’Andrea, Martín Sombra and Martin Weimann

Vol. 304 (2020), No. 2, 419–437
Abstract

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 in 3. 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.

Keywords
hypersurfaces, flex locus, multivariate resultants
Mathematical Subject Classification 2010
Primary: 14J70
Secondary: 13P15
Milestones
Received: 29 July 2019
Revised: 27 August 2019
Accepted: 27 August 2019
Published: 12 February 2020
Authors
Laurent Busé
Université Côte d’Azur, INRIA
Sophia Antipolis
France
Carlos D’Andrea
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Barcelona
Spain
Martín Sombra
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Barcelona
Spain
Institució Catalana de Recerca i Estudis Avançats (ICREA)
Barcelona
Spain
Martin Weimann
Laboratoire de mathématiques Nicolas Oresme, UMR CNRS 6139
University of Caen
Caen
France
Laboratoire de mathématiques GAATI
University of French Polynesia
Faaa
French Polynesia