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.
@article{bwmeta1.element.doi-10_1515_coma-2017-0006,
author = {Takumi Yamada},
title = {Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds},
journal = {Complex Manifolds},
volume = {4},
year = {2017},
pages = {73-83},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0006}
}
Takumi Yamada. Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds. Complex Manifolds, Tome 4 (2017) pp. 73-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0006/