On the postulation of a general projection of a curve inP
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Authors: | E Ballico Ph Ellia |
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Institution: | (1) Present address: Scuola Normale Superiore, 56100 Pisa, Italia;(2) Present address: Département de Mathématiques, CNRS LA 168, Université de Nice, Parc Valrose, 06034 Nice, France |
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Abstract: | Summary
We say that a curve C in
P
3
has maximal rank if for every integer k the restriction map rc(k):H
0(P
3, OP3(k)) H0 (C, OC(k))has maximal rank. Here we prove the following results. Theorem 1Fix integers g, d with 0g3,dg+3.Fix a curve X of genus g and L Picd (X).If g=3and X is hyperelliptic, assume d8. Let L(X)be the image of X by the complete linear system H
0(X, L). Then a general projection of L(X)into
P
3
has maximal rank. Theorem 2For every integer g0,there exists an integer d(g, 3)such that for every dd(g, 3),for every smooth curve X of genus g and every LPicd (X) the general projection of L(X)into
P
3
has maximal rank. |
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Keywords: | |
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