A characterization of certain Shimura curves in the moduli stack of abelian varieties

@inproceedings{Viehweg2002ACO,
  title={A characterization of certain Shimura curves in the moduli stack of abelian varieties},
  author={Eckart Viehweg and Kang Zuo},
  year={2002}
}
Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the non-flat (1,0) part of the corresponding variation of Hodge structures, the Arakelov inequalities say that 2deg(F(1,0)) is bounded from above by g=rank(F(1,0))(2q-2+s). We show that for s>0 families reaching this bound are isogenous to the g-fold product of a modular family of elliptic curves, and a constant abelian variety. For s=0, if… CONTINUE READING

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