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# On Shimura curves in the Torelli locus of curves

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Xin Lu (Mainz)

What SFB-Kolloquium Nov 21, 2013 from 03:15 pm to 04:15 pm Mainz, 05-432 (Hilbertraum) vCal iCal

Oort has conjectured there do not exist Shimura curves lie generically of Torelli locus of curves of genus $g \geq 8$.
We show that  there do not exist Shimura families of semi-stable curves of genus $g\geq 5$ over curves of Mumford type.

We also show that there do not exist Shimura curves, which lie generically in the Torelli locus of hyperelliptic curves of genus $g\geq 8$.
The first result proves a slight weaker form of the conjecture for the case of Shimura curves of Mumford type.
The second result proves the conjecture for the Torelli locus of hyperelliptic curves.