Boundedness in families with applications to arithmetic hyperbolicity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910362352222208 |
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| author | van Bommel, Raymond Javanpeykar, Ariyan Kamenova, Ljudmila |
| author_facet | van Bommel, Raymond Javanpeykar, Ariyan Kamenova, Ljudmila |
| contents | Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with nonzero irregularity. These results rely on the mild boundedness of semi-abelian varieties. We also introduce and study the notion of pseudo-algebraic hyperbolicity which extends Demailly's notion of algebraic hyperbolicity for projective schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_11225 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Boundedness in families with applications to arithmetic hyperbolicity van Bommel, Raymond Javanpeykar, Ariyan Kamenova, Ljudmila Algebraic Geometry Number Theory Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with nonzero irregularity. These results rely on the mild boundedness of semi-abelian varieties. We also introduce and study the notion of pseudo-algebraic hyperbolicity which extends Demailly's notion of algebraic hyperbolicity for projective schemes. |
| title | Boundedness in families with applications to arithmetic hyperbolicity |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/1907.11225 |