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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2403.07280 |
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Table des matières:
- Let $X$ be an algebraic surface with $\mathcal{L}$ an ample line bundle on $X$. Let $Γ(X, \mathcal{L})$ be the \emph{geometric monodromy} group associated to family of nonsingular curves in $X$ that are zero loci of sections of $\mathcal{L}$. We provide obstructions to $Γ(X, \mathcal{L})$ being finite index in the mapping class group. We also show that for any $k \ge 0$, the image of monodromy is finite index in appropriate subgroups of the quotient of the mapping class group by the $k$th term of the Johnson filtration assuming that $\mathcal{L}$ is sufficiently ample. This enables us to construct several subgroups of the mapping class group with unusual properties, in some cases providing the first examples of subgroups with those properties.