2022/05/02 by Kovács, Sándor J, Taji, Behrouz
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2205.00761
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.