Erratum for Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich’s conjecture$^\ast$

Abstract

We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is finite, and that this number is uniformly bounded in any finite type family of base varieties. As a corollary we show that a direct generalization of the geometric version of Shafarevich’s original conjecture holds for infinitesimally rigid families of canonically polarized varieties.

*This article was first printed in 172, 1719–1748.  This reprinting should be considered the version of record as it corrects a font error that resulted in notational problems throughout the paper.