Griffiths heights and pencils of hypersurfaces

2022/12/21 by Thomas Mordant, Mordant, Thomas · 2 citations
Mathematics · #14D07 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2212.11019

openalex publication_date 2022/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Pencils of projective hypersurfaces, Griffiths heights and geometric invariant theory. II Hypersurfaces with semihomogeneous singularities
• Pencils of projective hypersurfaces, Griffiths heights and geometric invariant theory. I

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