Teichmueller curves, Galois actions and GT-relations

2003/11/18 by Martin Moeller, Moeller, Martin
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0311308

22 pages

arxiv created 2004/10/11 · arxiv updated 2009/12/01

Abstract

Teichmueller curves are geodesic discs in Teichmueller space that project to algebraic curves C in the moduli space M_g. Some Teichmüller 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 π₁(C) with the one on π₁(M_g) and obtain a relation in the Grothendieck-Teichmueller group, seemingly independent of the known ones.

Related

• Variations of Hodge structures of a Teichmueller curve
• Hidden symmetries of the Grothendieck--Teichmüller group
• The Galois action on Hurwitz curves
• On Grothendieck's construction of Teichmüller space
• Actions of the Absolute Galois Group