The Jumping Phenomenon of the Dimensions of Cohomology Groups of Tangent Sheaf

2007/04/17 by Xuanming Ye, Ye, Xuanming
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.0704.2113

arxiv created 2007/04/17 · arxiv updated 2009/12/01

Abstract

Let X be a compact complex manifold, consider a small deformation ϕ: X → B of X, the dimensions of the cohomology groups of tangent sheaf H^q(X_t,T_Xt) may vary under this deformation. This paper will study such phenomenons by studying the obstructions to deform a class in H^q(X,T_X) with the parameter t and get the formula for the obstructions.

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