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The geometry of the flex locus of a hypersurface

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 P3. 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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https://hal.archives-ouvertes.fr/hal-01779785
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Submitted on : Thursday, April 26, 2018 - 11:09:41 PM
Last modification on : Friday, July 8, 2022 - 10:08:01 AM
Long-term archiving on: : Tuesday, September 25, 2018 - 8:33:50 AM

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Laurent Busé, Carlos d'Andrea, Martín Sombra, Martin Weimann. The geometry of the flex locus of a hypersurface. Pacific Journal of Mathematics, 2020, 304 (2), pp.419--437. ⟨10.2140/pjm.2020.304.419⟩. ⟨hal-01779785⟩

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