Extremal values of the basic invariants of plane curves

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	Extremal values of the basic invariants of plane curves
	Yu, JM; Zhou, JY; Pan, JZ
	2000-12-01
发表期刊	JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
ISSN	0218-2165
卷号	9 期号:8 页码:1085-1126
摘要	In [A2] V.I. Arnold introduced three basic invariants St, J(+) and J(-) of plane curves and proposed some interesting conjectures concerning the extremal values of these invariants on a given set of curves. Partial answers have been obtained by O. Viro and A.N. Shumakovich. We give explicit formulas for these extremal values of sets of plane curves with fixed number of double points and of Whitney index and we determine on which curves these extremal values are attained (Theorems 3-6). Our arguments are based on understanding of the fine structures of generic curves and some surgery operations on curves.
关键词	plane curves Arnold's invariants perestroikas surgery operations
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000166456300009
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15584
专题	中国科学院数学与系统科学研究院
通讯作者	Yu, JM
作者单位	Acad Sinica, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Yu, JM,Zhou, JY,Pan, JZ. Extremal values of the basic invariants of plane curves[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS,2000,9(8):1085-1126.
APA	Yu, JM,Zhou, JY,&Pan, JZ.(2000).Extremal values of the basic invariants of plane curves.JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS,9(8),1085-1126.
MLA	Yu, JM,et al."Extremal values of the basic invariants of plane curves".JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 9.8(2000):1085-1126.