Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture (vol 172, pg 1719, 2010)

• 成果类型: Correction
• 署名作者: Kovacs, Sandor J.; Lieblich, Max
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.1719
• 发表日期: 2011
• 页码: 585-617
• 关键词: general type; function-fields; VARIETIES; stacks; CURVES; MODULI; THEOREM

摘要

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.