The generality of a section of a curve

Let f: C --> P^3 be a general curve of genus g, mapped to via linear series degree d; and let Q (and thus smooth) quadric. In this paper, we show that the points intersection f(C) \cap give collection 2d on Q, except for exactly six exceptional cases. We also prove similar theorems every other pair (r, n) which, only finitely many pairs (d, g), g P^r d, with hypersurface S n, is dn S. As explained in arXiv:1809.05980, these results play key role author's proof Maximal Rank Conjecture