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

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

2007-04-17

arxiv.org/abs/0704.2113v1

Mathematics

Algebraic Geometry

Scientific paper

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 tangent sheaf $H^q(X_t,\mathcal{T}_{X_t})$ may vary under this deformation. This paper will 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 the obstructions.

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