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October 2010 Kobayashi geodesics in $A_g$
Martin Möller, Eckart Viehweg
J. Differential Geom. 86(2): 355-379 (October 2010). DOI: 10.4310/jdg/1299766791

Abstract

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 Teichmöller 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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Martin Möller. Eckart Viehweg. "Kobayashi geodesics in $A_g$." J. Differential Geom. 86 (2) 355 - 379, October 2010. https://doi.org/10.4310/jdg/1299766791

Information

Published: October 2010
First available in Project Euclid: 10 March 2011

zbMATH: 1218.14036
MathSciNet: MR2772554
Digital Object Identifier: 10.4310/jdg/1299766791

Rights: Copyright © 2010 Lehigh University

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Vol.86 • No. 2 • October 2010
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