Kobayashi geodesics in A_g

Details Kobayashi geodesics in A_g Kobayashi geodesics in A_g

2008-09-05

arxiv.org/abs/0809.1018v2

Mathematics

Algebraic Geometry

2nd version, AMSLATeX, 20 pages. We fixed a gap in the proof of Lemma 3.1. The main theorems of our preprint are unchanged

Scientific paper

We consider Kobayashi geodesics in the moduli space of abelian varieties A_g that is, algebraic curves that are totally geodesic submanifolds for the Kobayashi metric. We show that Kobayashi geodesics can be characterized as those curves whose logarithmic tangent bundle splits as a subbundle of the logarithmic tangent bundle of A_g. Both Shimura curves and Teichmueller curves are examples of Kobayashi geodesics, but there are other examples. We show moreover that non-compact Kobayashi geodesics always map to the locus of real multiplication and that the Q-irreducibility of the induced variation of Hodge structures implies that they are defined over a number field.

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