On the Gonality type invariants and the slope of a fibered $3$-fold
| Autor: | Akaike, Hiroto |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The \textit{slope} of a fibered $3$-folds $f:X \to B$ is a relative numerical invariant defined by $\lambda(f) := K_{f}^{3}/\mathrm{deg}(f_{\ast}\omega_{f})$, where $K_{f}$ is the relative canonical divisor and $\omega_{f}$ 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 $f$. Comment: 17 pages, comments are welcome! |
| Databáze: | arXiv |
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