Griffiths heights and pencils of hypersurfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912162308423680 |
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| author | Mordant, Thomas |
| author_facet | Mordant, Thomas |
| contents | The Griffiths height of a variation of Hodge structures over a projective curve is defined as the degree of its canonical line bundle, as defined by Griffiths and generalized by Peters to allow bad reduction points. It may be seen as a geometric analog of the Kato height attached to pure motives over number fields. In this paper, we establish various formulas expressing the Griffiths height of the middle-dimensional cohomology of a pencil of projective complex hypersurfaces in terms of characteristic classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11019 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Griffiths heights and pencils of hypersurfaces Mordant, Thomas Algebraic Geometry 14D07 The Griffiths height of a variation of Hodge structures over a projective curve is defined as the degree of its canonical line bundle, as defined by Griffiths and generalized by Peters to allow bad reduction points. It may be seen as a geometric analog of the Kato height attached to pure motives over number fields. In this paper, we establish various formulas expressing the Griffiths height of the middle-dimensional cohomology of a pencil of projective complex hypersurfaces in terms of characteristic classes. |
| title | Griffiths heights and pencils of hypersurfaces |
| topic | Algebraic Geometry 14D07 |
| url | https://arxiv.org/abs/2212.11019 |