Density of Noether-Lefschetz loci for surfaces in Fano and Calabi-Yau threefolds
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909364393082880 |
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| author | Mason, Edoardo |
| author_facet | Mason, Edoardo |
| contents | In this paper we provide applications of general results of Baldi-Klingler-Ullmo and Khelifa-Urbanik on the geometry of the Hodge locus associated to an integral polarized variation of Hodge structures to the case of Noether-Lefschetz loci for families of surfaces. In particular, we consider the family of surfaces in the linear system of a sufficiently ample line bundle on a smooth projective threefold $Y$, in case $Y$ is a Fano or a Calabi-Yau threefold, and we discuss the different behaviour of the union of the general, respectively exceptional, components of its Noether-Lefschetz locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density of Noether-Lefschetz loci for surfaces in Fano and Calabi-Yau threefolds Mason, Edoardo Algebraic Geometry In this paper we provide applications of general results of Baldi-Klingler-Ullmo and Khelifa-Urbanik on the geometry of the Hodge locus associated to an integral polarized variation of Hodge structures to the case of Noether-Lefschetz loci for families of surfaces. In particular, we consider the family of surfaces in the linear system of a sufficiently ample line bundle on a smooth projective threefold $Y$, in case $Y$ is a Fano or a Calabi-Yau threefold, and we discuss the different behaviour of the union of the general, respectively exceptional, components of its Noether-Lefschetz locus. |
| title | Density of Noether-Lefschetz loci for surfaces in Fano and Calabi-Yau threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.16974 |