On multisecants and the Green-Lazarsfeld index of projective varieties

초록

It is well known that a nondegenerate projective subvariety X subset of P(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.

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