English

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