Geodesic
Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich’s conjecture (PLEASE NOTE: The version of record for this article is published as an Erratum in Volume 173, no. 1, pp. 585–617.)
Sándor J. Kovács 1 ; Max Lieblich1
1 University of Washington<br/>Department of Mathematics<br/>Box 354350<br/>Seattle, WA 98195-4350<br/>United States
Annals of mathematics, Tome 172 (2010) no. 3, pp. 1719-1748.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.

Sándor J. Kovács  1 ; Max Lieblich 1

1 University of Washington<br/>Department of Mathematics<br/>Box 354350<br/>Seattle, WA 98195-4350<br/>United States 
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Sándor J. Kovács ; Max Lieblich. Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich’s conjecture (PLEASE NOTE:  The version of record for this article is published as an Erratum in Volume 173, no. 1, pp. 585–617.). Annals of mathematics, Tome 172 (2010) no. 3, pp. 1719-1748. http://geodesic.mathdoc.fr/item/AM_2010__172_3_a5/