论文标题
更高页面的鸡尾酒和AEPPLI共同体和应用
Higher-Page Bott-Chern and Aeppli Cohomologies and Applications
论文作者
论文摘要
对于每个正整数$ r $，我们介绍了两个新的共同体，它们称为$ e_r $ -bott-chern和$ e_r $ -aeppli，在紧凑的复杂歧管上。当$ r = 1 $时，它们与通常的Bott-Chern和Aeppli共同体相吻合，但是当$ r \ geq 2 $时，它们分别比这些。它们在歧管的frölicher频谱序列中提供的$ e_r $ nomologies的Bott-Chern-aeppli上下文中提供类似物。我们以多种方式应用了这些新的共同体来表征我们最近介绍的页面-（r-1）$ - $ \ partial \ bar \ partial $ -manifolds。我们还证明了这些较高页面的鸡巴和aeppli共同体以及Frölicher频谱序列中的空间的类似物。我们在研究冬形和强烈的高望台指标的研究中获得了一组我们的共同体应用，我们证明它们提供了自然的共同体学框架。
For every positive integer $r$, we introduce two new cohomologies, that we call $E_r$-Bott-Chern and $E_r$-Aeppli, on compact complex manifolds. When $r=1$, they coincide with the usual Bott-Chern and Aeppli cohomologies, but they are coarser, respectively finer, than these when $r\geq 2$. They provide analogues in the Bott-Chern-Aeppli context of the $E_r$-cohomologies featuring in the Frölicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page-$(r-1)$-$\partial\bar\partial$-manifolds that we introduced very recently. We also prove analogues of the Serre duality for these higher-page Bott-Chern and Aeppli cohomologies and for the spaces featuring in the Frölicher spectral sequence. We obtain a further group of applications of our cohomologies to the study of Hermitian-symplectic and strongly Gauduchon metrics for which we show that they provide the natural cohomological framework.
