Bounds on multisecant lines (Q1817878)

The paper deals with the following question: Let \(C\subseteq \mathbb{P}^3\) be a curve. What is the maximal order of a multisecant line to \(C\) in terms of natural invariants of \(C\), like the degree \(d\) and the genus \(g\)? From former results it is known that the maximal order is between 4 and \(d-1\) and both occur. The author is giving an upper bound on the order of the multisecant line to an integral arithmetically Cohen-Macaulay subscheme in \(\mathbb{P}^n\) of codimension 2 in terms of its Hilbert function. By examples it is shown that the bound is sharp.