Abstract
A method for exhibiting the equation of an algebraic curve for a large class of dessins on an orientable closed surface is developed, and the action of the absolute Galois group is realized as a modification of the associated cell structures. An application to quadratic differentials is discussed. A Galois invariant measure on ℂℙ(1) is introduced. Towers of (flat) refinements of dessins are introduced that relate the inverse system structure of the absolute Galois group to geometric/combinatorial structures on surfaces.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 6, pp. 145–159, 2013.
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Kamalinejad, A. On the Geometrization of the Absolute Galois Group. J Math Sci 209, 265–274 (2015). https://doi.org/10.1007/s10958-015-2501-7
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DOI: https://doi.org/10.1007/s10958-015-2501-7