The jumping phenomenon of the dimensions of cohomology groups of tangent sheaf

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• 作者：Ye Xuanming
• 关键词：dimensions of cohomology groups of tangent sheaf ; deformation ; obstruction ; Kodaira-Spencer class
• 刊名：Acta Mathematica Scientia
• 出版年：2010
• 出版时间：September 2010
• 年：2010
• 卷：30
• 期：5
• 页码：1746-1758
• 全文大小：269 K

文摘

Let X be a compact complex manifold. Consider a small deformation π: X → B of X, the dimensions of the cohomology groups of tangent sheaf H^q(X_t, TX_t) 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.