Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913527935008768 |
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| author | Latorre, A. Ugarte, L. Villacampa, R. |
| author_facet | Latorre, A. Ugarte, L. Villacampa, R. |
| contents | In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_14669 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics Latorre, A. Ugarte, L. Villacampa, R. Differential Geometry 53C55, 32J27, 53C15 In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici. |
| title | Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics |
| topic | Differential Geometry 53C55, 32J27, 53C15 |
| url | https://arxiv.org/abs/2207.14669 |