The push-forwards and pull-backs of δ-forms and applications to non-archimedean Arakelov geometry

2023/03/09 by Cai, Yulin
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.04978

Abstract

We study two kinds of push-forwards of δ-forms and define the pull-backs of δ-forms. As a generalization of Gubler-Künnemann, we prove the projection formula and the tropical Poincaré-Lelong formula. As an application, we follow the idea of Gubler-Künnemann and generalize the notion of δ-forms on algebraic varieties, this allows us to define the first Chern forms for any piecewise smooth metrics.

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• Positivity properties of metrics and delta-forms
• Formes différentielles réelles et courants sur les espaces de Berkovich
• Universal vector bundles, push-forward formulae and positivity of characteristic forms
• General Expressions for Chern Forms Up to the 13th Order in Curvature
• δ-Forms on Lubin--Tate Space