设X为一个紧致复流形,考虑\,$X$\,的任一复结构形变族 : X ! B ,则X的Bott-Chern上同调群和Aeppli上同调群的维数在此变化过程中可能产生跳跃现象. 在文献[1]中Schweitzer将Bott-Chern上同调群和Aeppli上同调群表示成为某一个层链 L•p,q的上同调群.在文献[2]中, 作者通过研究X各阶形变中与 L•p,q拟同构的层
链 B•p,q的超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. 本文将给出1阶障碍公式的另一个用 L•p,q上同调计算的解析证明.
Let X be a compact complex manifold, and let : X ! B be a small deformation of X, the dimensions of the Bott-Chern cohomology groups or Aeppli
cohomology groups may vary under this deformation. In [1], M. Schweitzer constructed a complex of sheaves L•p,q, and represented Bott-Chern cohomology groups or Aeppli cohomology groups as the cohomology groups of L•p,q. In [2], the author have studied this jumping phenomenon by studying the deformation obstructions of a hypercohomology class of a complex of sheaves B• p,q which is quasi-isomorphic to L• p,q[1]. In particular, they obtain an explicit formula for the obstructions. In this paper, the formula of the first order obstruction is proved in another way by using cohomology of L• p,q.
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