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- W3040494959 abstract "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 $rgeq 2$. They provide analogues in the Bott-Chern-Aeppli context of the $E_r$-cohomologies featuring in the Frolicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page-$(r-1)$-$partialbarpartial$-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 Frolicher 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." @default.
- W3040494959 created "2020-07-10" @default.
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- W3040494959 date "2020-07-07" @default.
- W3040494959 modified "2023-10-01" @default.
- W3040494959 title "Higher-Page Bott-Chern and Aeppli Cohomologies and Applications" @default.
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- W3040494959 doi "https://doi.org/10.48550/arxiv.2007.03320" @default.
- W3040494959 hasPublicationYear "2020" @default.
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