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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.00815 |
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| _version_ | 1866914868050788352 |
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| author | Ammar, Houari Benammar |
| author_facet | Ammar, Houari Benammar |
| contents | Let $f: S \longrightarrow C$ be a surjective morphism with connected fibers from a smooth complex projective surface $S$ to a smooth complex projective curve $C$ with general fiber $F$. In this paper, we develop a more general version of the slope inequality for data $(D, \mathcal{F})$, where $D$ is an arbitrary relatively effective divisor on $S$ and $\mathcal{F}$ is a locally free sub-sheaf of $f_{*}\mathcal{O}_{S}(D)$. We see how the speciality of $D$, restricted to the general fiber, plays a role in the results. Moreover, we compute some natural examples and provide applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00815 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slope inequality for an arbitrary divisor Ammar, Houari Benammar Algebraic Geometry Let $f: S \longrightarrow C$ be a surjective morphism with connected fibers from a smooth complex projective surface $S$ to a smooth complex projective curve $C$ with general fiber $F$. In this paper, we develop a more general version of the slope inequality for data $(D, \mathcal{F})$, where $D$ is an arbitrary relatively effective divisor on $S$ and $\mathcal{F}$ is a locally free sub-sheaf of $f_{*}\mathcal{O}_{S}(D)$. We see how the speciality of $D$, restricted to the general fiber, plays a role in the results. Moreover, we compute some natural examples and provide applications. |
| title | Slope inequality for an arbitrary divisor |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.00815 |