Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds

Details Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds

2009-10-05

arxiv.org/abs/0910.0815v2

Mathematics

Algebraic Geometry

12 pages. v2: Main Theorem slightly generalized to accommodate non-nefness

Scientific paper

The main result of this note is an effective uniform bound for the number of deformation types of certain nonisotrivial families of canonically polarized manifolds. It extends the author's earlier such bound for the classical Shafarevich Conjecture over function fields to the case of higher dimensional fibers, but without the disadvantageous iterated use of Chow or Hilbert varieties that was the core of the proofs in the earlier approaches.

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