Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture

Details Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture

2006-11-22

arxiv.org/abs/math/0611672v3

Mathematics

Algebraic Geometry

19 pages, v2: minor changes; one reference added to make a step cleaner and one name added to acknowledgements, v3: final vers

Scientific paper

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.

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