Resumen de Equations for the flex locus of a hypersurface

Laurent Busé, Carlos D'Andrea , Martín Sombra , Martin Weimann

• For a degree d surface in projective space with no ruled components, a theorem of Salmon asserts that the flex locus is a curve on this surface of degree at most 11d 2 −24d. We generalise this result to hypersurfaces of arbitrary dimension and compute explicit equations of the flex locus by using multidimensional resultant theory. For generic hypersurfaces, we show that our degree bound is reached and that the generic flex line is unique and with expected contact order.