Subvarieties of small codimension in smooth projective varieties

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	Subvarieties of small codimension in smooth projective varieties
其他题名	Subvarieties of small codimension in smooth projective varieties
	Li QiFeng
	2015
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	58 期号:3 页码:519-524
摘要	Let X subset of P-C(N) be an n-dimensional nondegenerate smooth projective variety containing an m-dimensional subvariety Y. Assume that either m > n/2 and X is a complete intersection or that m >= N/2. We show deg(X) vertical bar deg(Y) and codim( ) Y >= codim(PN) X, where is the linear span of Y. These bounds are sharp. As an application, we classify smooth projective n-dimensional quadratic varieties swept out by m >= n/2 + 1 dimensional quadrics passing through one point.
其他摘要	Let X ?P_C~N Cbe an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m>n/2 and X is a complete intersection or that m N≥2.We show deg(X)\|deg(Y)and codim ≥Y codim_(P~N) X, where is the linear span of Y.These bounds are sharp.As an application, we classify smooth projective n-dimensional quadratic varieties swept out by m≥n/2+1 dimensional quadrics passing through one point.
关键词	MANIFOLDS SWEPT LINES subvarieties small codimension degree
收录类别	CSCD
语种	英语
CSCD记录号	CSCD:5386940
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/53679
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Li QiFeng. Subvarieties of small codimension in smooth projective varieties[J]. SCIENCE CHINA-MATHEMATICS,2015,58(3):519-524.
APA	Li QiFeng.(2015).Subvarieties of small codimension in smooth projective varieties.SCIENCE CHINA-MATHEMATICS,58(3),519-524.
MLA	Li QiFeng."Subvarieties of small codimension in smooth projective varieties".SCIENCE CHINA-MATHEMATICS 58.3(2015):519-524.