- Main

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

- Author(s): Hartshorne, Robin
- Schlesinger, Enrico
- et al.

## Abstract

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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.