Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2017-02-23 DOI:10.1515/coma-2017-0006

Takumi Yamada

引用次数: 2

Abstract

Abstract Let N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.

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紧致幂零流形上Hodge数与不变复结构之间的一些关系

摘要:设N是一个单连通实数幂零李群，N是它的李代数，N是N上的一个格。如果N上的一个左不变复结构为Γ-rational，那么对于每一个s, HƏ′s,t(Γ/N)≃HƏ′s,t(nC);利用复化和标量限制，我们可以在一个幂零李群上构造不同的左不变复结构。研究了关联紧复零流形与霍奇数的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.