Archiv der Mathematik

, Volume 105, Issue 3, pp 229–237 | Cite as

Martens-Mumford theorems for Brill-Noether schemes arising from very ample line bundles

  • Ali Bajravani


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.

Mathematics Subject classification

Primary 14H99 Secondary 14H51 


Marthens–Mumford’s theorems Symmetric products Very ample line bundle 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Basic SciencesAzarbaijan Shahid Madani UniversityTabrizIslamic Republic of Iran

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