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1阶复结构形变中产生Bott-Chern上同调群和Aeppli上同调群维数跳跃的障碍公式的解析证明

, PP. 84-94

Keywords: Bott-Chern上同调群,Aeppli上同调群,复结构形变,障碍,?KodairaSpencer类

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Abstract:

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.

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