Curvature and relative volume forms

Luca Rizzi; Francesco Zucconi

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arXiv · 2504.08218

Curvature and relative volume forms

Luca Rizzi·Francesco Zucconi

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Abstract

Using metric techniques introduced by Berndtsson, we show a result on constancy of families dominated by a constant variety and, on the opposite side, a result on the strong non isotriviality of certain families of surfaces with positive index. We also give metric interpretations of liftability of relative volume forms and of strong non isotriviality in terms of the complex conjugate of a suitable representative of the Kodaira-Spencer class.

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Luca Rizzi, Francesco Zucconi. 2025-04-11. Curvature and relative volume forms. https://arxiv.org/abs/2504.08218

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