Towards a Halphen theory of linear series on curves

Details Towards a Halphen theory of linear series on curves Towards a Halphen theory of linear series on curves

1997-04-19

arxiv.org/abs/alg-geom/9704019v1

Mathematics

Algebraic Geometry

AMSTeX/AMSppt, 23 pages

Scientific paper

A linear series on a curve C in $P^3$ is "primary" when it does not contain the series cut by planes. We provide a lower bound for the degree of these series, in terms of deg(C), g(C) and of the number $s = min{i: h^0(I_C(i))\neq 0}$; as a corollary, we obtain bounds for the gonality of C. Examples show that our 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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