Counting projections of rational curves (Q2218724)

Given two general rational curves of the same degree in two projective spaces, the authors deal with the problem of deciding whether there exists a third rational curve of the same degree that projects to both of them. More precisely, it is proved that, under suitable assumptions on the degree of the curves and the dimensions of the given projective spaces, the number of curves and projections fulfilling the requirements is finite. The authors compute this number using standard techniques in intersection theory and the Bott residue formula.