Hyperbolicity and torsion in families of abelian varieties
Benjamin Bakker (Berlin)
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When 
Nov 05, 2015 from 03:30 pm to 04:30 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: The hyperbolicity of the moduli space Ag of abelian varieties implies that nontrivial families of abelian varieties exist over a quasiprojective curve B only when the Euler number χ(B) is negative. Conjecturally the existence of torsion sections of higher order requires the genus (or even the gonality) of B to be large. We investigate a general picture for understanding such phenomenaand prove the conjecture in a special caseby bounding Seshadri constants of the Hodge bundle along special subvarieties of the moduli space. Time permitting we will discuss a related result: that a family of elliptic curves over a base of fixed gonality is determined up to isogeny by its ptorsion local system. This is joint work with J. Tsimerman.