Complex Manifolds (Feb 2017)

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

  • Yamada Takumi

DOI
https://doi.org/10.1515/coma-2017-0006
Journal volume & issue
Vol. 4, no. 1
pp. 73 – 83

Abstract

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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.

Keywords