Remarks on the Clifford Index of Algebraic Curves

Abstract

$\mathrm{Cliff}(X)$ be the Clifford index of a curve $X$ and $L$ be a base-point-free line bundle on $X$ which satisfies $\mathrm{Cliff}(L) = \mathrm{Cliff}(X) + k (k \geq 3)$. We determine sufficient conditions for the $|L| = g^{r}_{d}$ being simple (i.e. birationally very ample).