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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.00926 |
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| _version_ | 1866917053783343104 |
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| author | Chen, Meng Jiang, Zhi |
| author_facet | Chen, Meng Jiang, Zhi |
| contents | For all nonsingular projective $n$-folds $V$ of general type, we prove the existence of Noether type inequalities in the following form: $$\text{vol}(V)\geq a_{n,k}h^0(Ω_V^k)-b_{n,k}$$ where $0< k\leq n$, $a_{n,k}$ and $b_{n,k}$ are positive constants only depending on $n$ and $k$. As applications, we prove the minimal volume conjecture for $3$-folds of general type with $χ({\mathcal O})\neq 2,3$ and disclose a new type of lifting principles for the sequence of canonical stability indices for varieties of general type. Finally we prove a theorem about ``strong lifting principle'' on varieties $V$ of general type with $q>\dim(V)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00926 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On general type varieties admitting global holomorphic forms Chen, Meng Jiang, Zhi Algebraic Geometry For all nonsingular projective $n$-folds $V$ of general type, we prove the existence of Noether type inequalities in the following form: $$\text{vol}(V)\geq a_{n,k}h^0(Ω_V^k)-b_{n,k}$$ where $0< k\leq n$, $a_{n,k}$ and $b_{n,k}$ are positive constants only depending on $n$ and $k$. As applications, we prove the minimal volume conjecture for $3$-folds of general type with $χ({\mathcal O})\neq 2,3$ and disclose a new type of lifting principles for the sequence of canonical stability indices for varieties of general type. Finally we prove a theorem about ``strong lifting principle'' on varieties $V$ of general type with $q>\dim(V)$. |
| title | On general type varieties admitting global holomorphic forms |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2211.00926 |