Secant planes of a general curve via degenerations

Cotterill Ethan; He Xiang; Zhang Naizhen

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Secant planes of a general curve via degenerations

机译：通过退化剪切一般曲线的平面

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摘要

We study linear series on a general curve of genusg, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded by anincludedlinear series, whose number of base points computes the incidence degree of the corresponding secant plane. With enumerative applications in mind, we construct a moduli scheme of inclusions of limit linear series with base points over families of nodal curves of compact type, which we then use to compute combinatorial formulas for the number of secant-exceptional linear series when the spaces of linear series and of inclusions are finite.

机译：我们研究了genusg一般曲线上的线性级数，其图像相对于其割线平面而言是例外的。每个这样的异常割线平面都由一个包含的线性序列进行代数编码，其基点的数量计算相应割线平面的关联度。考虑到枚举应用，我们构造了紧致型节点曲线族上带基点的极限线性级数包含的模格式，然后当线性级数和包含的空间有限时，我们用它来计算割线例外线性级数的个数的组合公式。

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来源
《European Journal of Medicinal Chemistry: Chimie Therapeutique》 |2021年第1期|共37页
作者
Cotterill Ethan; He Xiang; Zhang Naizhen;
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作者单位

Univ Fed Fluminense Inst Matemat Rua Prof Waldemar Freitas S-N Campus Gragoata BR-24210201;

Hebrew Univ Jerusalem Einstein Inst Math Edmond J Safra Campus IL-9190401 Jerusalem Israel;

Leibniz Univ Hannover Inst Differentialgeometrie Welfengarten 1 D-30167 Hannover Germany;

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原文格式 PDF
正文语种 eng
中图分类药学;
关键词
Moduli of curves; Linear series; Degenerations;

机译：曲线模量;线性级数;退化;

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5. Secant planes of a general curve via degenerations [J] . Cotterill Ethan, He Xiang, Zhang Naizhen Geometriae Dedicata . 2021,第1期

机译：通过退化剪切一般曲线的平面
6. Geometry of curves with exceptional secant planes: linear series along the general curve [J] . Ethan Cotterill Mathematische Zeitschrift . 2011,第s3a4期

机译：具有特殊割平面的曲线的几何形状：沿着一般曲线的线性序列
7. Geometry of curves with exceptional secant planes: Linear series along the general curve [J] . Cotterill E. Mathematische Zeitschrift . 2011,第3a4期

机译：具有特殊割平面的曲线的几何形状：沿着一般曲线的线性序列
8. Effect of a secant film on a curved circular plate coupled with viscosity variation and MHD effect [C] . E. Sujatha, E. P. Siva International Conference on Mathematical Techniques and Applications . 2020

机译：截线膜对曲面变异和MHD效应的弯曲圆形板上的影响
9. Enumerative geometry of curves with exceptional secant planes. [D] . Cotterill, Ethan Guy. 2007

机译：具有特殊割线平面的曲线的枚举几何。
10. A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area [O] . Michael C. Dallaston, Scott W. McCue -1

机译：封闭区域中具有指定变化率的闭合嵌入式平面曲线的曲线缩短流规则
11. Geometry of curves with exceptional secant planes: linear series along the general curve [O] . Cotterill, Ethan 2010

机译：具有特殊割线面的曲线几何：线性系列一般曲线
12. Secant Varieties and Successive Minima. Appendix: On Linear Subspaces Contained in the Secant Varieties of a Projective Curve. [R] . Soule, C., Voisin, C. 2001

机译：正确的品种和连续的极小。附录：关于投影曲线的正割变量中包含的线性子空间。

Secant planes of a general curve via degenerations

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