Special Linear Systems on Algebraic Curves

代数曲线上的特殊线性系统

• 批准号: 13640029
• 负责人: OHBUCHI Akira
• 金额: $ 1.6万
• 依托单位: The University of Tokushima
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640029/
• 关键词: Algebraic Curve; Brill-Noether Theory; special linear system; Brill-Nother理論

Let C be a smooth algebraic curve. Assume that C does not admit a double covering to another curve when C is an eve-gonal curve. We proved that if the dimension of a family of line bundles with degree d in which d is less than g-5, is more than d-3r-2, then C is a d-gonal curve with d【less than or equal】6, a 4-sheeted covering of an elliptic curve or a plane curve of degree 8. This is our first result. Next, in case 6-gonal we can prove that except a triple covering of an elliptic curve, the dimension of a family of line bundles with degree d in which d is less than g-5, should be less than d-3r-3, and in case 4-sheeted covering of an elliptic curve, the same conclusion holds.

设C是一条光滑的代数曲线。假设当C是一条多边形曲线时，C不允许对另一条曲线进行双重覆盖。证明了如果d次线束族的维数d < g-5 > d-3r-2，则C是d <≤6的d形曲线，是椭圆曲线或8次平面曲线的四层覆盖。这是我们的第一个结果。其次，我们可以证明，除了椭圆曲线的三重覆盖外，d次线束族的维数d小于g-5的维数应该小于d-3r-3，对于椭圆曲线的四层覆盖，同样的结论成立。

项目成果

A. Ohbuchi et al.: "Proceedings of the Symposium on Algebraic Geometry in East Asia"World Scientific. (2003)

A. Ohbuchi 等人：“东亚代数几何研讨会论文集”世界科学。

T. Kato: "Martens' dimension theorem for curves of even gonality."Korean J. Math.. {\bf 39}, 5. 665-680 (2002)

T. Kato：“偶数曲线的马滕斯维数定理”。Korean J. Math.. {f 39}, 5. 665-680 (2002)

M.Homma, A.Ohbuchi: "Plane curves with aligned conductors"Far East Journal of Mathematical Sciences. 4(1). 21-53 (2002)

M.Homma、A.Ohbuchi：“具有对齐导体的平面曲线”远东数学科学杂志。

K-H. Cho, C. Keem, A. Ohbuchi: "On the variety of special linear systems of degree $g-1$ on smooth algebraic curves"International Journal of Math.. 13, No1. 11-29 (2002)

K-H。

K-H.Cho, C.Keem, A.Ohbuchi: "On the variety of special linear systems of degree g-1 on smooth algebraic curves"International Journal of Math.. 13(1). 11-29 (2002)

K-H.Cho、C.Keem、A.Ohbuchi：“关于光滑代数曲线上 g-1 次特殊线性系统的多样性”国际数学杂志 13(1)。