E. Schlesinger: Gonality of a general ACM curve in projective space.

Abstract. Let C be an ACM (projectively normal) nonsingular curve in P³ not contained in a plane, and suppose C is general in its Hilbert scheme - this is irreducible once the postulation is fixed.

Answering a question by Peskine in the case of a general ACM curve, we show the gonality of C is d-m, where d is the degree of the curve, and m is the maximum order of a multisecant to C.

Furthermore m=4 except for rare cases, when the postulation of C forces every surface of minumum degree containing C to contain a line as well. We compute the value of m in these exceptional cases as well.

Joint work with R. Hartshorne.