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

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• 作者：Ali Bajravani
• 关键词：Primary 14H99 ; Secondary 14H51 ; Marthens–Mumford’s theorems ; Symmetric products ; Very ample line bundle
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：105
• 期：3
• 页码：229-237
• 全文大小：465 KB
• 参考文献：1.Aprodu M., Sernesi E.: Secant spaces and syzygies of special line bundles on curves. Algebra and Number Theory 9, 585-00 (2015)MathSciNet CrossRef
  2.E. Arbarello et?al., Geometry of Algebraic Curves, I. Grundlehren 267 (1985), Springer, Berlin.
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  4.M. Coppens, Some remarks on the Scheme \({W^{r}_{d}}\) , Annali di Matem. P. e A. 97,(1990), 183-97.
  5.C. Keem, A remark on the Variety of Special Linear Systems on an Algebraic Curve, Ph. D. Thesis, Brown University (1983).
  6.Macdonald I. G.: Symmetric Products of an Algebraic Curve. Topology 1, 319-43 (1962)MathSciNet CrossRef MATH
  7.Martens H. H.: On the Varieties of special Divisors on a Curve. J. Reine Angew. Math. 227, 111-20 (1967)MathSciNet MATH
  8.D. Mumford, Prym Varieties I, In Contributions to Analysis (L. V. Ahlfors, I. Kra, B. Maskit, L. Nireremberg, eds.), Academic Press, New York, (1974), 325-50.
  
• 作者单位：Ali Bajravani (1)
  
  1. Department of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, P. O. Box: 53751-71379, Tabriz, Islamic Republic of Iran
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

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