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arXiv · 2205.00761

Arakelov inequalities in higher dimensions

Sándor J Kovács·Behrouz Taji
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Abstract

We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves. We show that for families of manifolds with ample canonical bundle this invariant is uniformly bounded. As a consequence we establish that such families over a base of arbitrary dimension verify the aforementioned Arakelov inequality, answering a question of Viehweg.

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Sándor J Kovács, Behrouz Taji. 2022-05-02. Arakelov inequalities in higher dimensions. https://arxiv.org/abs/2205.00761

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