#### Vol. 304, No. 2, 2020

 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
Primary: 14J70
Secondary: 13P15