The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties

Abstract

Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of polarized varieties. We then give an arithmetic application to the finiteness of integral points on moduli spaces of polarized varieties.

17 pages. Minor corrections and improvements

References in corpus (7)

• Logarithmic Geometry and Moduli
• Boundedness in families with applications to arithmetic hyperbolicity
• Generic positivity and applications to hyperbolicity of moduli spaces
• The Shafarevich conjecture for hypersurfaces in abelian varieties
• Pseudo Kobayashi hyperbolicity of base spaces of families of minimal projective manifolds with maximal variation
• Good reduction and cyclic covers
• Finiteness properties of pseudo-hyperbolic varieties

Cited by in corpus (4)

• Boundedness in families with applications to arithmetic hyperbolicity
• Good reduction and cyclic covers
• Finiteness properties of pseudo-hyperbolic varieties
• Non-archimedean hyperbolicity of the moduli space of curves