Title: On separable higher Gauss maps,
Abstract: We study the $m$-th Gauss map in the sense of F.~L.~Zak of a projective
variety $X \subset \mathbb{P}^N$ over an algebraically closed field in any
characteristic. For all integer $m$ with $n:=\dim(X) \leq m < N$, we show that
the contact locus on $X$ of a general tangent $m$-plane is a linear variety if
the $m$-th Gauss map is separable. We also show that for smooth $X$ with $n <
N-2$, the $(n+1)$-th Gauss map is birational if it is separable, unless $X$ is
the Segre embedding $\mathbb{P}^1 \times \mathbb{P}^n \subset
\mathbb{P}^{2n-1}$. This is related to L. Ein's classification of varieties
with small dual varieties in characteristic zero.