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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08089 |
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| _version_ | 1866911200155009024 |
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| author | Xu, Shi |
| author_facet | Xu, Shi |
| contents | Let $D$ be a big integral divisor on a smooth projective surface $X$. In this paper, we study Noether-type inequalities for $D$. The key ingredient is the introduction of a numerical invariant $\mathfrak{e}(D)$, which depends only on the negative part $N$ of $D$. In particular, $\mathfrak{e}(D)=0$ if $D$ is nef. As an application, we establish an inequality between the volume and the pluri-sectional index of a canonical foliated surface of general type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noether-Type Inequalities for Big Divisors on Algebraic Surfaces Xu, Shi Algebraic Geometry Let $D$ be a big integral divisor on a smooth projective surface $X$. In this paper, we study Noether-type inequalities for $D$. The key ingredient is the introduction of a numerical invariant $\mathfrak{e}(D)$, which depends only on the negative part $N$ of $D$. In particular, $\mathfrak{e}(D)=0$ if $D$ is nef. As an application, we establish an inequality between the volume and the pluri-sectional index of a canonical foliated surface of general type. |
| title | Noether-Type Inequalities for Big Divisors on Algebraic Surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2510.08089 |