Arakelov inequalities in higher dimensions
Algebraic Geometry
2022-10-12 v2
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.
Cite
@article{arxiv.2205.00761,
title = {Arakelov inequalities in higher dimensions},
author = {Sándor J Kovács and Behrouz Taji},
journal= {arXiv preprint arXiv:2205.00761},
year = {2022}
}
Comments
Streamlined exposition; minor changes in notations; additional details and references in Section 2