Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1746-1758.doi: 10.1016/S0252-9602(10)60168-3

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THE JUMPING PHENOMENON OF THE DIMENSIONS OF COHOMOLOGY GROUPS OF TANGENT SHEAF

 YE Xuan-Ming   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2007-03-14 Revised:2008-10-30 Online:2010-09-20 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.

Abstract:

Let X be a compact complex manifold. Consider a small deformation πχ→ B of X, the dimensions of the cohomology groups of tangent sheaf
H q(XtTXt) may vary under this deformation. This article  studies such phenomena by studying the obstructions to deform a class in H q(XTX) with parameter t and gets a formula for the obstructions.

Key words: dimensions of cohomology groups of tangent sheaf, deformation, obstruction, Kodaira-Spencer class

CLC Number: 

  • 32G05
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