Canonical extensions of manifolds with nef tangent bundle
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911389784735744 |
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| author | Müller, Niklas |
| author_facet | Müller, Niklas |
| contents | To any compact Kähler manifold $(X, ω)$ one may associate a bundle of affine spaces $Z_X\rightarrow X$ called a \emph{canonical extension} of $X$. In this paper we prove that if the tangent bundle of $X$ is nef, then the total space $Z_X$ is a Stein manifold. This partially answers a question raised by Greb-Wong of whether these two properties are actually equivalent. We also complement some known results for surfaces in the converse direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03469 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Canonical extensions of manifolds with nef tangent bundle Müller, Niklas Algebraic Geometry To any compact Kähler manifold $(X, ω)$ one may associate a bundle of affine spaces $Z_X\rightarrow X$ called a \emph{canonical extension} of $X$. In this paper we prove that if the tangent bundle of $X$ is nef, then the total space $Z_X$ is a Stein manifold. This partially answers a question raised by Greb-Wong of whether these two properties are actually equivalent. We also complement some known results for surfaces in the converse direction. |
| title | Canonical extensions of manifolds with nef tangent bundle |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2211.03469 |