An Analytic Proof for the Formula of the First Order Obstruction Making the Hodge Numbers Jumping

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- An Analytic Proof for the Formula of the First Order Obstruction Making the Hodge Numbers Jumping
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 51, Issue 6, (2012)
- 作者机构：
  
  1. 广州大学数学与信息科学学院∥数学与交叉学科广东普通高校重点实验室,广东,广州,510006
  2. 中山大学数学与计算科学学院,广东,广州,510275
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2012，
  
  Published Online：25 November 2012，
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LIN Jiezhu, YE Xuanming. An Analytic Proof for the Formula of the First Order Obstruction Making the Hodge Numbers Jumping. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 51(6).(2012)
DOI：

LIN Jiezhu, YE Xuanming. An Analytic Proof for the Formula of the First Order Obstruction Making the Hodge Numbers Jumping. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 51(6).(2012) DOI：

设X为一个紧致复流形，考虑X的任一复结构形变族π：χ→B，则X的微分形式层的上同调群H

t，

)的维数在此变化过程中可能产生跳跃现象。相关文献作者通过研究X各阶形变中微分形式层的上同调群等价类元素在延拓过程中的障碍来研究这一跳跃现象，得到了产生此障碍的公式。文中将给出1阶障碍公式的另一个用Dolbeault上同调计算的证明。

Let X be a compact complex manifold

and let π:χ→B be a small deformation of X

the dimensions of the Dolbeault cohomology groups H

) may vary under this deformation. The author studied the deformation obstructions of a (p

q) class in the central fiber X. In particular

He obtained an explicit formula for the obstructions. The first order obstruction is proved in another way by using Dolbeault cohomology.

Hodge数复结构形变障碍Kodaira Spencer类

Hodge numberdeformationobstructionKodaira Spencer class

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