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The Griffiths height of a variation of Hodge structures over a projectivecurve is defined as the degree of its canonical line bundle, as defined byGriffiths and generalized by Peters to allow bad reduction points. It may beseen as a geometric analog of the Kato height attached to pure motives overnumber fields. In this paper, we establish various formulas expressing theGriffiths height of the middle-dimensional cohomology of a pencil of projectivecomplex hypersurfaces in terms of characteristic classes.

Griffiths heights and pencils of hypersurfaces