Higher-page Bott-Chern and Aeppli cohomologies and applications
For every positive integer r, we introduce two new cohomologies, that we call Er-Bott–Chern and Er-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≥2. They provide analogues in...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Zaragoza |
| Repositorio: | Zaguán. Repositorio Digital de la Universidad de Zaragoza |
| OAI Identifier: | oai:zaguan.unizar.es:130900 |
| Acceso en línea: | http://zaguan.unizar.es/record/130900 |
| Access Level: | acceso abierto |
| Sumario: | For every positive integer r, we introduce two new cohomologies, that we call Er-Bott–Chern and Er-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≥2. They provide analogues in the Bott–Chern–Aeppli context of the Er-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)-∂¯∂-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. |
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