  We address the question of counting maps between projective spaces such that
images of cycles on the source intersect cycles on the target. In this paper we
do it by embedding maps into quasimaps that form a projective space of their
own. When a quasimap is not a map, it contains freckles (studied earlier)
and/or scars, appearing when the complex dimension of the source is greater
than one. We consider a lot of examples showing that freckle/scar calculus
(using excess intersection theory) works. We also propose the "smooth
conjecture" that may lead to computation of the number of maps by an integral
over the space of quasimaps.
