The geometry of the flex locus of a hypersurface
Algebraic Geometry
2020-02-12 v3 Commutative Algebra
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. 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
Cite
@article{arxiv.1804.08025,
title = {The geometry of the flex locus of a hypersurface},
author = {Laurent Busé and Carlos D'Andrea and Martin Sombra and Martin Weimann},
journal= {arXiv preprint arXiv:1804.08025},
year = {2020}
}
Comments
16 pages. This paper has been accepted for publication in the Pacific Journal of Mathematics