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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2210.01087 |
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| _version_ | 1866916495355805696 |
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| author | Lombardi, Luigi Schnell, Christian |
| author_facet | Lombardi, Luigi Schnell, Christian |
| contents | We prove that a torsion-free sheaf $\mathcal F$ endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition $\mathcal F \simeq \mathcal U \oplus \mathcal A$ where $\mathcal U$ is a hermitian flat bundle and $\mathcal A$ is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles $f_* ω_{X/Y}^{\otimes m}$ under a surjective morphism $f\colon X \to Y$ of smooth projective varieties with $m\geq 2$. This extends previous results of Fujita, Catanese--Kawamata, and Iwai. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01087 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata Lombardi, Luigi Schnell, Christian Algebraic Geometry We prove that a torsion-free sheaf $\mathcal F$ endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition $\mathcal F \simeq \mathcal U \oplus \mathcal A$ where $\mathcal U$ is a hermitian flat bundle and $\mathcal A$ is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles $f_* ω_{X/Y}^{\otimes m}$ under a surjective morphism $f\colon X \to Y$ of smooth projective varieties with $m\geq 2$. This extends previous results of Fujita, Catanese--Kawamata, and Iwai. |
| title | Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2210.01087 |