On the distribution of ramification points in trigonal curves (Q1587805)

Let \(C\) be a trigonal curve of genus \(g\geq 5\), defined over an algebraically closed field \(k\) of characteristic 0. A point \(P\in C\) is said a total ramification point of the \(g^1_3\) on \(C\) if \(3P\in g^1_3\). In the paper under review, the author studies ramification points of the trigonal covering via the canonical models which lie on a rational normal scroll \(S\). He finds bounds and relations for the total ramification points that lie on the intersection with a rational curve of \(S\), by considering whether or not such curve is the directrix of \(S\).