A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
@article{bwmeta1.element.doi-10_1515_coma-2015-0012, author = {Takumi Yamada}, title = {Duality of Hodge numbers of compact complex nilmanifolds}, journal = {Complex Manifolds}, volume = {2}, year = {2015}, zbl = {1333.53072}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0012} }
Takumi Yamada. Duality of Hodge numbers of compact complex nilmanifolds. Complex Manifolds, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0012/
[1] C. Benson and C. S. Gordon, K¨ahler and symplectic structures on nilmanifolds, Topology 27 (1988), 513–518. [Crossref] | Zbl 0672.53036
[2] S. Console and A. Fino, Dolbeault cohomology of compact nilmanifolds, Transform. Groups 6 (2001), 111–124. [Crossref]
[3] L.A. Cordero, M, Fern´andez and A. Gray, Symplectic manifolds with no K¨ahler structure, Topology 25 (1986), 375–380. [Crossref]
[4] L.A. Cordero, M, Fern´andez, and L. Ugarte, Lefschetz complex conditions for complex manifolds, Ann. Global Anal. Geom. 22 (2002), 355–373. | Zbl 1030.53072
[5] R. Goto, Moduli space of topological calibrations, Calami-Yau, hyperK¨ahler, G2, spin(7) structures, International Journal of Mathematices., 15 (2004), 211–257.
[6] R. Goto, Deformations of holomorphic symplectic structures on nil and solvmanifolds (in Japanese), Proceeding of Workshop of Differential geometry in Osaka University, (2006), 54–64.
[7] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106, (1989), 65–71. | Zbl 0691.53040
[8] I. Nakamura, Complex parallelisable manifolds and their small deformations, J. Differential Geom. 10 (1975), 85–112. | Zbl 0297.32019
[9] Y. Sakane, On compact complex parallelisable solvmanifolds, Osaka J. Math. 13 (1976), 187–212. | Zbl 0361.22005
[10] S.M. Salamon, Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra 157 (2001), 311–333. | Zbl 1020.17006
[11] T. Yamada, Complex structures and non-degenerate closed 2-forms of compact real parallelizable pseudo-K¨ahler nilmanifolds, preprint.