Kollár's package for polystable locally abelian parabolic Higgs bundles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916738592931840 |
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| author | Shentu, Junchao Zhao, Chen |
| author_facet | Shentu, Junchao Zhao, Chen |
| contents | We generalize Kollár's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an $\mathbb{R}$-divisor. This gives a uniform treatment for various kinds of Kollár's package in different topics in complex geometry. As applications, the weakly positivity (in the sense of Viehweg) and the generic vanishing property for higher direct image sheaves are deduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kollár's package for polystable locally abelian parabolic Higgs bundles Shentu, Junchao Zhao, Chen Algebraic Geometry We generalize Kollár's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an $\mathbb{R}$-divisor. This gives a uniform treatment for various kinds of Kollár's package in different topics in complex geometry. As applications, the weakly positivity (in the sense of Viehweg) and the generic vanishing property for higher direct image sheaves are deduced. |
| title | Kollár's package for polystable locally abelian parabolic Higgs bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.17636 |