Journal of East China Normal University(Natural Sc ›› 2015, Vol. 2015 ›› Issue (1): 84-94.doi: 10.3969/j.issn.1000-5641.2015.01.010

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An analytic proof for the formula of the first order obstruction making the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups jumping

 LIN  Jie-Zhu1, YE  Xuan-Ming2   

  1. 1. School of Mathematics And Information Science, Guangzhou University, Key Laboratory of Mathematics, and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou 510006, China;
    2. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2014-03-01 Online:2015-01-25 Published:2015-03-29

Abstract: Let X be a compact complex manifold, and let  : X ! B be a small deformation of X, the dimensions of the Bott-Chern cohomology groups or Aeppli
cohomology groups may vary under this deformation. In [1], M. Schweitzer constructed a complex of sheaves L•p,q, and represented Bott-Chern cohomology groups or Aeppli cohomology groups as the cohomology groups of L•p,q. In [2], the author have studied this jumping phenomenon by studying the deformation obstructions of a hypercohomology class of a complex of sheaves B• p,q which is quasi-isomorphic to L• p,q[1]. In particular, they obtain an explicit formula for the obstructions. In this paper, the formula of the first order obstruction is proved in another way by using cohomology of L• p,q.

Key words: Bott-Chern cohomology, Aeppli cohomology, deformation, obstruction, kodaira spencer class

CLC Number: