Mok's characteristic varieties and the normal holonomy group

详细信息    查看全文

• 作者：Antonio J. Di Scala^a ; ¹ ; ^{antonio.discala@polito.it} ; ; Francisco Vittone^b ; ² ; ³ ; ^{vittone@fceia.unr.edu.ar} ;
• 关键词：53C29 ; 53C40
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：987-1008
• 全文大小：430 K
• 卷排序：308

文摘

In this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of CnCn or CPnCPn. We show that irreducible but non-transitive normal holonomies are exactly the Hermitian s-representations of [4, Table 1] (see Corollary 1.1). For each one of them we construct a non necessarily complete complex submanifold whose normal holonomy is the prescribed s-representation.We also show that if the submanifold has irreducible non-transitive normal holonomy then it is an open subset of the smooth part of one of the characteristic varieties studied by N. Mok in his work about rigidity of locally symmetric spaces.Finally, we prove that if the action of the normal holonomy group of a projective submanifold is reducible then the submanifold is an open subset of the smooth part of a so called join, i.e. the union of the lines joining two projective submanifolds.