On the variety of linear series on a singular curve

Ballico, E. ; Fontanari, C.

Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 631-639

Résumé

Let $Y$ be an integral projective curve with $g := p_{a}(Y) \geq 2$. For all positive integers $d$, $r$ let $W^{r}_{d}(Y)(\text{}^{**})$ be the set of all $L \in \text{Pic}^{d}(Y)$ with $h^{0}(Y, L) \geq r+1$ and $L$ spanned. Here we prove that if $d \leq g-2$, then $\dim (W^{r}_{d}(Y) (\text{}^{**})) \leq d-3r$ except in a few cases (essentially if $Y$ is a double covering).