Acta mathematica scientia, Series B >
THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF
Received date: 2007-03-14
Revised date: 2008-10-30
Online published: 2010-09-20
Supported by
The research was partially supported by China-France-Russian mathematics collaboration grant, No. 34000-3275100, from Sun Yat-Sen University.
Let X be a compact complex manifold. Consider a small deformation π: χ→ B of X, the dimensions of the cohomology groups of tangent sheaf
H q(Xt, TXt) may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in H q(X, TX) with parameter t and gets a formula for the obstructions.
YE Xuan-Ming . THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1746 -1758 . DOI: 10.1016/S0252-9602(10)60168-3
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