$L^2$ Frölicher inequalities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911077546065920 |
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| author | Bei, Francesco Piovani, Riccardo |
| author_facet | Bei, Francesco Piovani, Riccardo |
| contents | We prove a Frölicher inequality between $L^2$ Betti and $L^2$ Hodge numbers on normal coverings of compact complex manifolds. This is achieved by building an injection using suitable spectral projectors associated to the self adjoint operators $(D_h)^2:=(\overline\partial+\overline\partial^*+h\partial+h\partial^*)^2$ for $h\in[0,1]$. As a by-product, we find a new proof of the classical Frölicher inequality on compact complex manifolds which does not rely at all on spectral sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^2$ Frölicher inequalities Bei, Francesco Piovani, Riccardo Differential Geometry Complex Variables Geometric Topology 32Q55, 58J10 We prove a Frölicher inequality between $L^2$ Betti and $L^2$ Hodge numbers on normal coverings of compact complex manifolds. This is achieved by building an injection using suitable spectral projectors associated to the self adjoint operators $(D_h)^2:=(\overline\partial+\overline\partial^*+h\partial+h\partial^*)^2$ for $h\in[0,1]$. As a by-product, we find a new proof of the classical Frölicher inequality on compact complex manifolds which does not rely at all on spectral sequences. |
| title | $L^2$ Frölicher inequalities |
| topic | Differential Geometry Complex Variables Geometric Topology 32Q55, 58J10 |
| url | https://arxiv.org/abs/2507.19385 |