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-Zhu; YE Xuan-Ming

doi:10.3969/j.issn.1000-5641.2015.01.010

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LIN Jie-Zhu, YE Xuan-Ming. An analytic proof for the formula of the first order obstruction making the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups jumping[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 84-94. doi: 10.3969/j.issn.1000-5641.2015.01.010

Citation:

LIN Jie-Zhu, YE Xuan-Ming. An analytic proof for the formula of the first order obstruction making the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups jumping[J]. Journal of East China Normal University (Natural Sciences), 2015, (1): 84-94. doi: 10.3969/j.issn.1000-5641.2015.01.010

Citation:

LIN Jie-Zhu, YE Xuan-Ming. An analytic proof for the formula of the first order obstruction making the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups jumping[J]. Journal of East China Normal University (Natural Sciences), 2015, (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

doi: 10.3969/j.issn.1000-5641.2015.01.010

LIN Jie-Zhu¹,
YE Xuan-Ming^{2
,
,}

1.
School of Mathematics And Information Science, Guangzhou University, Key Laboratory of Mathematics, and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou 510006, China;

Received Date: 2014-03-01
Publish Date: 2015-01-25

Abstract

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 Lp,q, and represented Bott-Chern cohomology groups or Aeppli cohomology groups as the cohomology groups of Lp,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.
- Bott-Chern cohomology,
- Aeppli cohomology,
- deformation,
- obstruction,
- kodaira spencer class

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References(1)

References

[1]

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