On the postulation of a general projection of a curve in \(P^ N\), N\(\geq 4\) (Q1096692)

Main results: (a) Fix integers N, d, g with \(N>3\), \(0\leq g\leq N-1\), \(d\geq g+N\), a smooth curve X of genus \(g\) and \(L\in Pic^ d(X)\); let \(h_ L(X)\) be the image of X by the complete linear system \(H^ 0(X,L)\); then a general projection of \(H_ L(X)\) into \({\mathbb{P}}^ N\) has maximal rank. \((b)\quad Fix\) N, g with \(N>3\), \(g\geq 0\); there is an integer d(g,N) such that for every \(d\geq d(g,N)\), for every smooth curve X of genus \(g\) and every \(L\in Pic{}^ d(X)\), the general projection of \(h_ L(X)\) into \({\mathbb{P}}^ N\) has maximal rank. The case \(N=3\) was done by the authors in Ann. Mat. Pura Appl., IV. Ser. 142, 15-48 (1985; Zbl 0591.14041)].