Description
The $k$-flex locus of a projective hypersurface $V\subset \mathbb P^n$ is the locus of points $p\in V$ such that there is a line with order of contact at least $k$ with $V$ at $p$.
Unexpected contact orders occur when $k\ge n+1$. The case $k=n+1$ is known as the classical flex locus, which has been studied in details in the literature. In this talk I will present a joint work with Martin Weimann (Caen), dedicated to compute the dimension and the degree of the $k$-flex locus of a general degree $d$ hypersurface for any value of $k$.