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Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, I
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 121, Number 2, April 1999
- pp. 315-358
- 10.1353/ajm.1999.0015
- Article
- Additional Information
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 M0,4, M0,5, M1,1 and M1,2 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" /].