数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1746-1758.doi: 10.1016/S0252-9602(10)60168-3

• 论文 • 上一篇    下一篇

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

叶轩明   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • 收稿日期:2007-03-14 修回日期:2008-10-30 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    The research was partially supported by China-France-Russian mathematics collaboration grant, No. 34000-3275100, from Sun Yat-Sen University.

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.

摘要:

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.

关键词: dimensions of cohomology groups of tangent sheaf, deformation, obstruction, Kodaira-Spencer class

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

中图分类号: 

  • 32G05