一阶复结构形变中产生Hodge数跳跃的障碍公式的解析证明

摘要

Let X be a compact complex manifold, and let π:x→ B be a small deformation of X, the dimensions of the Dolbeault cohomology groups Hp(Xt ,Ωpxt) may vary under this deformation. The author studied the deformation obstructions of a (p, q) class in the central fiber X. In particular, He obtained an explicit formula for the obstructions. The first order obstruction is proved in another way by using Dolbeault cohomology.%设X为一个紧致复流形,考虑X的任一复结构形变族π:x→B,则X的微分形式层的上同调群H(ρ)(X(t),Ω(ρ)X(t))的维数在此变化过程中可能产生跳跃现象.相关文献作者通过研究X各阶形变中微分形式层的上同调群等价类元素在延拓过程中的障碍来研究这一跳跃现象,得到了产生此障碍的公式.文中将给出1阶障碍公式的另一个用Dolbeault上同调计算的证明.