# Arithmetic hyperbolicity

Date(s) : 14/02/2017   iCal
11 h 00 min - 12 h 00 min

We will show that, assuming Lang-Vojta’s conjecture, the moduli of smooth hypersurfaces of fixed degree in a fixed projective space is arithmetically hyperbolic. More generally, any algebraic stack with an immersive period map is arithmetically hyperbolic assuming Lang-Vojta’s conjecture.
We finish with unconditional results. For instance, we verify the arithmetic hyperbolicity of the moduli of smooth sextic surfaces, and certain Fano threefolds. We also give a first explicit counterexample to Shafarevich’s problem for Fano threefolds.
This is joint work with Daniel Loughran.

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