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Complex Manifolds

Ed. by Fino, Anna Maria

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Mathematical Citation Quotient (MCQ) 2016: 0.67


Emerging Science

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2300-7443
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Duality of Hodge numbers of compact complex nilmanifolds

Takumi Yamada
  • Corresponding author
  • Department of Mathematics, Shimane University, Nishikawatsu-cho 1060, Matsue, 690-8504, Japan
  • Other articles by this author:
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Published Online: 2015-12-07 | DOI: https://doi.org/10.1515/coma-2015-0012

Abstract

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.

Keywords: nilmanifold; Dolbeault cohomology group; complex structure

References

  • [1] C. Benson and C. S. Gordon, K¨ahler and symplectic structures on nilmanifolds, Topology 27 (1988), 513–518. CrossrefGoogle Scholar

  • [2] S. Console and A. Fino, Dolbeault cohomology of compact nilmanifolds, Transform. Groups 6 (2001), 111–124. CrossrefGoogle Scholar

  • [3] L.A. Cordero, M, Fern´andez and A. Gray, Symplectic manifolds with no K¨ahler structure, Topology 25 (1986), 375–380. CrossrefGoogle Scholar

  • [4] L.A. Cordero, M, Fern´andez, and L. Ugarte, Lefschetz complex conditions for complex manifolds, Ann. Global Anal. Geom. 22 (2002), 355–373. Google Scholar

  • [5] R. Goto, Moduli space of topological calibrations, Calami-Yau, hyperK¨ahler, G2, spin(7) structures, International Journal of Mathematices., 15 (2004), 211–257. Google Scholar

  • [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. Google Scholar

  • [7] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106, (1989), 65–71. Google Scholar

  • [8] I. Nakamura, Complex parallelisable manifolds and their small deformations, J. Differential Geom. 10 (1975), 85–112. Google Scholar

  • [9] Y. Sakane, On compact complex parallelisable solvmanifolds, Osaka J. Math. 13 (1976), 187–212. Google Scholar

  • [10] S.M. Salamon, Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra 157 (2001), 311–333. Google Scholar

  • [11] T. Yamada, Complex structures and non-degenerate closed 2-forms of compact real parallelizable pseudo-K¨ahler nilmanifolds, preprint. Google Scholar

About the article

Received: 2015-08-10

Accepted: 2015-11-20

Published Online: 2015-12-07


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0012.

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© 2015 Takumi Yamada. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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