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Abstract
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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
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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.
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Keywords
hypersurfaces, flex locus, multivariate resultants
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Mathematical Subject Classification 2010
Primary: 14J70
Secondary: 13P15
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Milestones
Received: 29 July 2019
Revised: 27 August 2019
Accepted: 27 August 2019
Published: 12 February 2020
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