  For a smooth complete intersection X, we consider a general fiber \mathbb{F}
of the evaluation map ev of Kontsevich moduli space
\bar{M}_{0,m}(X,m)\rightarrow X^m and the forgetful functor F : \mathbb{F}
\rightarrow \bar{M}_{0,m}. We prove that a general fiber of the map $F$ is a
smooth complete intersection if $X$ is of low degree. The result sheds some
light on the arithmetic and geometry of Fano complete intersections.
