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arXiv · 2212.11019

Griffiths heights and pencils of hypersurfaces

Thomas Mordant
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Abstract

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.

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Thomas Mordant. 2024-12-20. Griffiths heights and pencils of hypersurfaces. https://arxiv.org/abs/2212.11019

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