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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.11246 |
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| _version_ | 1866929493625536512 |
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| author | Baldi, Gregorio Klingler, Bruno Ullmo, Emmanuel |
| author_facet | Baldi, Gregorio Klingler, Bruno Ullmo, Emmanuel |
| contents | We study when the Picard group of smooth surfaces of degree $d\geq 5$ in $\mathbb{P}^3$ acquires extra classes. In particular we show that the so called exceptional components of the Noether-Lefschetz locus are not Zariski dense. This answers a 1991 question of C. Voisin. We also obtain similar results for the Noether-Lefschetz locus for suitable $(Y,L)$, where $Y$ is a smooth projective threefold and $L$ a very ample line bundle. Both results are applications of the Zilber-Pink viewpoint recently developed by the authors for arbitrary (polarized, integral) variations of Hodge structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11246 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-density of the exceptional components of the Noether-Lefschetz locus Baldi, Gregorio Klingler, Bruno Ullmo, Emmanuel Algebraic Geometry We study when the Picard group of smooth surfaces of degree $d\geq 5$ in $\mathbb{P}^3$ acquires extra classes. In particular we show that the so called exceptional components of the Noether-Lefschetz locus are not Zariski dense. This answers a 1991 question of C. Voisin. We also obtain similar results for the Noether-Lefschetz locus for suitable $(Y,L)$, where $Y$ is a smooth projective threefold and $L$ a very ample line bundle. Both results are applications of the Zilber-Pink viewpoint recently developed by the authors for arbitrary (polarized, integral) variations of Hodge structures. |
| title | Non-density of the exceptional components of the Noether-Lefschetz locus |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.11246 |