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

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

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 c...

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Bibliographic Details
Main Author: Yamada Takumi
Format: Article
Language:English
Published: De Gruyter 2017-02-01
Series:Complex Manifolds
Subjects:
nilmanifold
dolbeault cohomology group
complex structure
53c30
22e25
Online Access:https://doi.org/10.1515/coma-2017-0006
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spelling doaj-8adb3cad5d3c4186bb689b384fb9b8a32021-09-06T19:19:41ZengDe GruyterComplex Manifolds2300-74432017-02-0141738310.1515/coma-2017-0006coma-2017-0006Some relations between Hodge numbers and invariant complex structures on compact nilmanifoldsYamada Takumi0Department of Mathematics, Shimane University, Nishikawatsu-cho 1060, Matsue, 690-8504, JapanLet 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.https://doi.org/10.1515/coma-2017-0006nilmanifolddolbeault cohomology groupcomplex structure53c3022e25
collection DOAJ
language English
format Article
sources DOAJ
author Yamada Takumi
spellingShingle Yamada Takumi
Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
Complex Manifolds
nilmanifold
dolbeault cohomology group
complex structure
53c30
22e25
author_facet Yamada Takumi
author_sort Yamada Takumi
title Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
title_short Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
title_full Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
title_fullStr Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
title_full_unstemmed Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds
title_sort some relations between hodge numbers and invariant complex structures on compact nilmanifolds
publisher De Gruyter
series Complex Manifolds
issn 2300-7443
publishDate 2017-02-01
description 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.
topic nilmanifold
dolbeault cohomology group
complex structure
53c30
22e25
url https://doi.org/10.1515/coma-2017-0006
work_keys_str_mv AT yamadatakumi somerelationsbetweenhodgenumbersandinvariantcomplexstructuresoncompactnilmanifolds
_version_ 1717778068992425984

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