Gonality of a general ACM curve in projective 3-space

Details Gonality of a general ACM curve in projective 3-space Gonality of a general ACM curve in projective 3-space

2008-12-09

arxiv.org/abs/0812.1634v1

Mathematics

Algebraic Geometry

Pdf-latex, 2 pdf figures, 42 pages

Scientific paper

Let C be an ACM (projectively normal) nondegenerate smooth curve in projective 3-space, and suppose C is general in its Hilbert scheme - this is irreducible once the postulation is fixed. Answering a question posed by Peskine, we show the gonality of C is d-l, where d is the degree of the curve, and l is the maximum order of a multisecant line of C. Furthermore l=4 except for two series of cases, in which the postulation of C forces every surface of minimum degree containing C to contain a line as well. We compute the value of l in terms of the postulation of C in these exceptional cases. We also show the Clifford index of C is equal to the gonality minus 2.

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