Variations of Hodge structures of a Teichmueller curveReport as inadecuate



 Variations of Hodge structures of a Teichmueller curve


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Teichmueller curves are geodesic discs in Teichmueller space that project to an algebraic curve in the moduli space $M g$. We show that for all $g \geq 2$ Teichmueller curves map to the locus of real multiplication in the moduli space of abelian varieties. Remark that McMullen has shown that precisely for $g=2$ the locus of real multiplication is stable under the $\SL 2\RR$-action on the tautological bundle $\Omega\M g$. We also show that Teichmueller curves are defined over number fields and we provide a completely algebraic description of Teichmueller curves in terms of Higgs bundles. As a consequence we show that the absolute Galois group acts on the set of Teichmueller curves.



Author: Martin Moeller

Source: https://archive.org/







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