مشخصات پژوهش

‎Tangent spaces of $V_{d}^{r}(L)$'s‎, ‎specific subschemes of $C_{d}$ arising from various line bundles $L$ on $C$‎, ‎are described‎. ‎Then we proceed to prove Martens theorem for these schemes‎, ‎by which we determine curves $C$‎, ‎which for some very ample line bundle $L$ on $C$ and some integers $r$ and $d$ with $d\leq h^{0}(L)-2$‎, ‎the scheme $V_{d}^{r}(L)$ might attain its maximum dimension‎.