Plane algebraic curves with many cusps, with an appendix by Eugenii Shustin
Plane algebraic curves with many cusps, with an appendix by Eugenii Shustin
复制标题
具有多个尖点的平面代数曲线，附录由 Eugenii Shustin 绘制
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Ezio Stagnaro
中科院分区：
文献类型：
--
作者：
A. Calabri;Diego Paccagnan;Ezio Stagnaro
d次平面代数曲线上尖点的最大个数k（d）是一个经典的开放问题，可以追溯到世纪。一个相关的开放问题是渐近值（$$a. v.$$）平面曲线上尖点的数量，即$$a. v.= limsup _{d
ightarrow infty } k（d）/{d^2}$$。在本文中，我们提高了最好的已知的渐近值的下限，通过构造曲线的最大已知数的尖点无穷多次。还构造了一些特殊的低次多尖点曲线。本文的“附录”专门讨论11度的情况，这是由于E.舒斯汀。
The maximum number $$k(d)$$ of cusps on a plane algebraic curve of degree $$d$$ is an open classical problem that dates back to the nineteenth century. A related open problem is the asymptotic value ($$a.v.$$) of the number of cusps on plane curves, that is $$a.v.=limsup _{d
ightarrow infty } k(d)/{d^2}$$. In this paper, we improve the best known lower bound for the asymptotic value by constructing curves with the largest known number of cusps for infinitely many degrees. Some particular curves of relatively low degree with many cusps are constructed too. The “Appendix” to this paper is devoted to the case of degree 11 and it is due to E. Shustin.
尖端平面曲线、syzygies 和 MW 等级的界限
DOI：
10.1016/j.jalgebra.2012.11.015
发表时间：
2013
期刊：
arXiv: Algebraic Geometry
影响因子：
--
作者：
R. Kloosterman
通讯作者：
R. Kloosterman