Secant planes of a general curve via degenerations (Q2664079)

In this paper, Osserman's theory of limit linear series, as a generalization of that of Eisenbud-Harris for compact type curves, is reviewed. Built on that, two constructions of a moduli space of inclusions of limit linear series are provided. Both spaces agree set-theoretically, but the second one, described as an intersection of determinantal loci of vector bundles helps proving a smoothing theorem for inclusion of limit linear series in special cases. Based on this, explicit formulas for counting inclusion of limit linear series, and equivalently for the number of secant planes to the image of a curve under a map are calculated. The paper ends with an example showing that the moduli of included limit linear series may have a component of unexpectedly large dimension. Reviewer's remark: In Definition 4.1, the divisor \(D\) seems undefined -- perhaps \(Y\) may have been intended?