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Mathematics > Algebraic Geometry

arXiv:1804.08025 (math)
[Submitted on 21 Apr 2018 (v1), last revised 28 Aug 2019 (this version, v3)]

Title:The geometry of the flex locus of a hypersurface

Authors:Laurent Busé, Carlos D'Andrea, Martin Sombra, Martin Weimann
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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.
Comments: 16 pages. This paper has been accepted for publication in the Pacific Journal of Mathematics
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 14J70, 13P15
Cite as: arXiv:1804.08025 [math.AG]
  (or arXiv:1804.08025v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1804.08025
Journal reference: Pacific J. Math. 304 (2020) 419-437
Related DOI: https://doi.org/10.2140/pjm.2020.304.419

Submission history

From: Martin Weimann [view email]
[v1] Sat, 21 Apr 2018 20:51:13 UTC (18 KB)
[v2] Wed, 31 Jul 2019 00:27:24 UTC (18 KB)
[v3] Wed, 28 Aug 2019 18:31:58 UTC (18 KB)
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