Parametrization of rational maps on a variety of general type, and the finiteness theorem

In a previous paper we provided some update in the treatment of
the finiteness theorem for rational maps of finite degree from a fixed variety to
varieties of general type. In the present paper we present another improvement,
introducing the natural parametrization of maps by means of the space of linear
projections in a suitable projective space, and this leads to some new insight
into the geometry of the finiteness theorem.