  This paper is to give some concrete examples of the general fibers of the
evaluation map of some Kontsevich mapping spaces parametrize low degree
rational curves on low degree complete intersection varieties. We prove these
examples are Fano or Calabi-Yau vareities of low dimension, e.g, surface and
threefold. In usual, the "moduli" fibers are constructed in an abstract way,
but here we give a down-to-earth interpretation to some of these fibers from
the perspective of projective geometry.
