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Abstract
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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.
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