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

Takumi Yamada 1
  • 1 Department of Mathematics, Shimane University, Nishikawatsu-cho 1060, , Matsue, Japan

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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