Abstract
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 the theorem of Martens 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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Bajravani, A. Martens-Mumford theorems for Brill-Noether schemes arising from very ample line bundles. Arch. Math. 105, 229–237 (2015). https://doi.org/10.1007/s00013-015-0805-y
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DOI: https://doi.org/10.1007/s00013-015-0805-y