On the Gonality type invariants and the slope of a fibered $3$-fold
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917633361707008 |
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| author | Akaike, Hiroto |
| author_facet | Akaike, Hiroto |
| contents | The \textit{slope} of a fibered $3$-folds $f:X \to B$ is a relative numerical invariant defined by $λ(f) := K_{f}^{3}/\mathrm{deg}(f_{\ast}ω_{f})$, where $K_{f}$ is the relative canonical divisor and $ω_{f}$ is the relative dualizing sheaf. Establishing slope inequalities is a fundamental problem in the geography of fibered spaces. In this paper, we introduce a new invariant called the \textit{minimal covering degree} as a gonality-type invariant and study a lower bound of the slope increasing with the covering gonality and the minimal covering degree of the general fiber of $f$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_05216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Gonality type invariants and the slope of a fibered $3$-fold Akaike, Hiroto Algebraic Geometry Primary 14D06, Secondary 14J10, 14J30 The \textit{slope} of a fibered $3$-folds $f:X \to B$ is a relative numerical invariant defined by $λ(f) := K_{f}^{3}/\mathrm{deg}(f_{\ast}ω_{f})$, where $K_{f}$ is the relative canonical divisor and $ω_{f}$ is the relative dualizing sheaf. Establishing slope inequalities is a fundamental problem in the geography of fibered spaces. In this paper, we introduce a new invariant called the \textit{minimal covering degree} as a gonality-type invariant and study a lower bound of the slope increasing with the covering gonality and the minimal covering degree of the general fiber of $f$. |
| title | On the Gonality type invariants and the slope of a fibered $3$-fold |
| topic | Algebraic Geometry Primary 14D06, Secondary 14J10, 14J30 |
| url | https://arxiv.org/abs/2404.05216 |