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Let $X$ be a compact complex manifold, consider a small deformation $\phi:\mathcal{X} \to B$ of $X$, the dimensions of the cohomology groups of tangentsheaf $H^q(X_t,\mathcal{T}_{X_t})$ may vary under this deformation. This paperwill study such phenomenons by studying the obstructions to deform a class in$H^q(X,\mathcal{T}_X)$ with the parameter $t$ and get the formula for theobstructions.

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