A linear series g^N on a curve C in P3 is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree , in terms of deg(C), g(C) and of the number s = min{i : h^0I_C(i) > 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.
Chiantini, L., Ciliberto, C. (1999). Towards a Halphen theory of linear series on curves. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 351(6), 2197-2212 [10.1090/S0002-9947-99-01949-2].
Towards a Halphen theory of linear series on curves
CHIANTINI, LUCA;
1999-01-01
Abstract
A linear series g^N on a curve C in P3 is primary when it does not contain the series cut by planes. For such series, we provide a lower bound for the degree , in terms of deg(C), g(C) and of the number s = min{i : h^0I_C(i) > 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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https://hdl.handle.net/11365/37498
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