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Existence results for rational normal curves

In this paper we study existence of rational normal curves in ℙn passing through p points and intersecting l codimension‐two linear spaces in n − 1 points each. If p + l = n + 3 and the points and the linear spaces are general, then one expects the curve to exist, but this is not always the case. For p > 0, our main result precisely describes in which cases the curve exists and in which it does not exist. Moreover, when there is existence we also show that the curve is unique.