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

On enumerative problems for maps and quasimaps: freckles and scars