Remarks on the Clifford index of algebraic curves (Q2479945)

Let \(X\) be a smooth curve of genus \(g \geq 4\). Let \(\text{Cliff}(X)\) be its Clifford index. Here the author gives conditions on a base-point-free line bundle \(L\) on \(X\) which assure that \(L\) is birationally very ample. All statements are sharp, e.g. if \(L\) is a \(g^r_d\), \(r \geq 3\), \(g-1-d+r \geq 1\), and \(\text{Cliff}(L) =\text{Cliff} (X) +4\), then \(L\) is birationally very ample, except \(5\) exceptional pairs \((X,L)\).