Duality of Hodge numbers of compact complex nilmanifolds

Takumi Yamada

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 168-177, electronic only
  • ISSN: 2300-7443

Abstract

top
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.

How to cite

top

Takumi Yamada. "Duality of Hodge numbers of compact complex nilmanifolds." Complex Manifolds 2.1 (2015): 168-177, electronic only. <http://eudml.org/doc/275851>.

@article{TakumiYamada2015,
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.},
author = {Takumi Yamada},
journal = {Complex Manifolds},
keywords = {nilmanifold; Dolbeault cohomology group; complex structure},
language = {eng},
number = {1},
pages = {168-177, electronic only},
title = {Duality of Hodge numbers of compact complex nilmanifolds},
url = {http://eudml.org/doc/275851},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Takumi Yamada
TI - Duality of Hodge numbers of compact complex nilmanifolds
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 168
EP - 177, electronic only
AB - 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.
LA - eng
KW - nilmanifold; Dolbeault cohomology group; complex structure
UR - http://eudml.org/doc/275851
ER -

References

top
  1. [1] C. Benson and C. S. Gordon, K¨ahler and symplectic structures on nilmanifolds, Topology 27 (1988), 513–518. [Crossref] Zbl0672.53036
  2. [2] S. Console and A. Fino, Dolbeault cohomology of compact nilmanifolds, Transform. Groups 6 (2001), 111–124. [Crossref] 
  3. [3] L.A. Cordero, M, Fern´andez and A. Gray, Symplectic manifolds with no K¨ahler structure, Topology 25 (1986), 375–380. [Crossref] 
  4. [4] L.A. Cordero, M, Fern´andez, and L. Ugarte, Lefschetz complex conditions for complex manifolds, Ann. Global Anal. Geom. 22 (2002), 355–373. Zbl1030.53072
  5. [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. [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. [7] K. Hasegawa, Minimal models of nilmanifolds, Proc. Amer. Math. Soc. 106, (1989), 65–71. Zbl0691.53040
  8. [8] I. Nakamura, Complex parallelisable manifolds and their small deformations, J. Differential Geom. 10 (1975), 85–112. Zbl0297.32019
  9. [9] Y. Sakane, On compact complex parallelisable solvmanifolds, Osaka J. Math. 13 (1976), 187–212. Zbl0361.22005
  10. [10] S.M. Salamon, Complex structures on nilpotent Lie algebras, J. Pure Appl. Algebra 157 (2001), 311–333. Zbl1020.17006
  11. [11] T. Yamada, Complex structures and non-degenerate closed 2-forms of compact real parallelizable pseudo-K¨ahler nilmanifolds, preprint. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.