Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, I

Abstract

We study Gal[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-actions on the fundamental groups arising in deformation of maximally degenerate marked curves, and give explicit descriptions of them in terms of the principal parameters of the Grothendieck-Teichmüller group [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]. As a special application, we present Galois theoretic connections between the moduli spaces M 0,4 , M 0,5 , M 1,1 and M 1,2 which lead to a newtype equation satisfied by the image of Gal[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /].