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

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 Hq(Xt, TXt) may vary under this deformation. This article studies such phenomena by studying the obstructions to deform a class in Hq(X, TX) with parameter t and gets a formula for the obstructions.