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

DOI: 10.2140/pjm.2020.304.419

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 ${\P }^3$. 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