Let C be an ACM (projectively normal) nonsingular curve in ℙ^3 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 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 gon(C) − 2.
Gonality of a general ACM curve in P^3
SCHLESINGER, ENRICO ETTORE MARCELLO
2011-01-01
Abstract
Let C be an ACM (projectively normal) nonsingular curve in ℙ^3 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 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 gon(C) − 2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
