  Let K be an algebraically closed field of characteristic zero. We say that a
polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal
to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of
fixed points of a non-trivial special polynomial automorphism f : K^n -> K^n is
uniruled. Moreover, we show that if f is non-special and H is an
(n-1)-dimensional component of the set Fix(f), then H is smooth, irreducible
and H = Fix(f) and for K = C the Euler characteristic of H is equal to 1.
