Curvature of higher direct images of sheaves of twisted holomorphic forms
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913418268639232 |
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| author | Choi, Young-Jun Schumacher, Georg |
| author_facet | Choi, Young-Jun Schumacher, Georg |
| contents | This paper investigates the curvature properties of higher direct images $ R^qf_*Ω_{X/S}^p(E)$, where $f: X\rightarrow S$ is a family of compact Kähler manifolds equipped with a hermitian vector bundle $E \rightarrow X$. We derive a general curvature formula and explore several special cases, including those where $p + q = n$, $q = 0$, and $p = n$, with $E$ being a line bundle. Furthermore, the paper examines the curvature in the context of fiberwise hermitian flat cases, families of Hermite-Einstein vector bundles, and applications to moduli spaces and Weil-Petersson metrics, providing some insight into their geometric and analytical properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature of higher direct images of sheaves of twisted holomorphic forms Choi, Young-Jun Schumacher, Georg Complex Variables Algebraic Geometry Differential Geometry 32L10, 14D20, 32G05 This paper investigates the curvature properties of higher direct images $ R^qf_*Ω_{X/S}^p(E)$, where $f: X\rightarrow S$ is a family of compact Kähler manifolds equipped with a hermitian vector bundle $E \rightarrow X$. We derive a general curvature formula and explore several special cases, including those where $p + q = n$, $q = 0$, and $p = n$, with $E$ being a line bundle. Furthermore, the paper examines the curvature in the context of fiberwise hermitian flat cases, families of Hermite-Einstein vector bundles, and applications to moduli spaces and Weil-Petersson metrics, providing some insight into their geometric and analytical properties. |
| title | Curvature of higher direct images of sheaves of twisted holomorphic forms |
| topic | Complex Variables Algebraic Geometry Differential Geometry 32L10, 14D20, 32G05 |
| url | https://arxiv.org/abs/2407.04298 |