GONALITY OF A GENERAL ACM CURVE IN P3

被引：10

作者：

Hartshorne, Robin ^{[1
]}

Schlesinger, Enrico ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[2] Politecn Milan, Dipartimento Matemat F Brioschi, I-20122 Milan, Italy

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2011年 / 251卷 / 02期

关键词：

gonality; Clifford index; ACM space curves; multisecant lines; CLIFFORD INDEX; NOETHER; VARIETIES; MANIFOLDS; SURFACE; THEOREM; IDEALS; PETRI;

D O I：

10.2140/pjm.2011.251.269

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let C be an ACM (projectively normal) nonsingular curve in P-C(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.

引用

页码：269 / 313

页数：45

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