On multisecants and the Green-Lazarsfeld index of projective varieties

摘要

It is well known that a nondegenerate projective subvariety X ? ?~r of degree d and codimension c > 1 has minimal degree (i.e., d = c + 1) if and only if index(X) ≥ c if and only if X has no multisecant c-space. In this paper we extend this result by classifying varieties with index(X) ≥ c - s or with no multisecant (c - s)-space for s = 1 and 2.