Teichmueller curves, Galois actions and GT-relations

Details Teichmueller curves, Galois actions and GT-relations Teichmueller curves, Galois actions and GT-relations

2003-11-18

arxiv.org/abs/math/0311308v2

Mathematics

Algebraic Geometry

22 pages

Scientific paper

Teichmueller curves are geodesic discs in Teichmueller space that project to algebraic curves $C$ in the moduli space $M_g$. Some Teichm\"uller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group $G_\QQ$ acts faithfully on the set of these embedded curves. We also compare the action of $G_\QQ$ on $\pi_1(C)$ with the one on $\pi_1(M_g)$ and obtain a relation in the Grothendieck-Teichmueller group, seemingly independent of the known ones.

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