Towards a Halphen theory of linear series on curves

Chiantini, L.; Ciliberto, C.

doi:10.1090/S0002-9947-99-01949-2

Towards a Halphen theory of linear series on curves
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by L. Chiantini and C. Ciliberto

Trans. Amer. Math. Soc. 351 (1999), 2197-2212

DOI: https://doi.org/10.1090/S0002-9947-99-01949-2

Published electronically: March 1, 1999

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Abstract:

A linear series $g^{N}_{\delta }$ on a curve $C\subset \mathbf {P}^{3}$ is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree $\delta$, in terms of deg($C$), g($C$) and of the number $s=\min \{i:h^{0}\mathcal {I}_{C}(i)\neq 0\}$. Examples show that the bound is sharp. Extensions to the case of general linear series and to the case of curves in higher projective spaces are considered.

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