2008/12/09 by Robin Hartshorne, Hartshorne, Robin, Enrico Schlesinger +1
Computer Science · Mathematics · #14H50 #14H51 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H50 #msc:14H51
paper · pdf · doi:10.48550/arxiv.0812.1634
Pdf-latex, 2 pdf figures, 42 pages
arxiv created 2008/12/09 · openalex publication_date 2008/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.