  In this paper, we relate the set of asymptotic critical values of a
polynomial function $f$ with the set of discontinuity of two functions, the
multivalued function which associate to each value $t$ the set of tangent
directions at infinity of the fiber $f^{-1}(t)$ and the composition of the
$(n-2)$-dimensional volume function with the first one. This gives necessary
conditions of equisingularity at infinity for the family of the fibers of a
real polynomial function.
