Existence and density of typical Hodge loci
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914862894940160 |
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| author | Khelifa, Nazim Urbanik, David |
| author_facet | Khelifa, Nazim Urbanik, David |
| contents | Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable $\mathbb{Z}$-variation of Hodge structures $\mathbb{V}$. Our criterion reproves the existing results in the literature on density of Noether-Lefschetz loci. It also applies to understand Hodge loci of subvarieties of $\mathcal{A}_g$ . For instance, we prove that for $g \geq 4$, if a subvariety $S$ of $\mathcal{A}_g$ has dimension at least $g$ then it has an analytically dense typical Hodge locus. This applies for example to the Torelli locus of $\mathcal{A}_g$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16179 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence and density of typical Hodge loci Khelifa, Nazim Urbanik, David Algebraic Geometry Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge loci associated to a polarizable $\mathbb{Z}$-variation of Hodge structures $\mathbb{V}$. Our criterion reproves the existing results in the literature on density of Noether-Lefschetz loci. It also applies to understand Hodge loci of subvarieties of $\mathcal{A}_g$ . For instance, we prove that for $g \geq 4$, if a subvariety $S$ of $\mathcal{A}_g$ has dimension at least $g$ then it has an analytically dense typical Hodge locus. This applies for example to the Torelli locus of $\mathcal{A}_g$ |
| title | Existence and density of typical Hodge loci |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2303.16179 |