2006/05/10 by Ingrid Bauer, Fabrizio Catanese, Bauer, Ingrid +3
Mathematics · #11R32 #11S05 #12D99 #14J10 #14J29 #14M99 #20D99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:11R32 #msc:11S05 #msc:12D99 #msc:14J10 #msc:14J29 #msc:14M99 #msc:20D99
paper · pdf · doi:10.48550/arxiv.math/0605258
25 pages, to appear in the Special Volume of Mediterranean Journal of Mathematics, dedicated to the Almeria Mediterranean Congress of Mathematics, 2005
arxiv created 2006/05/10 · openalex publication_date 2006/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We start discussing the group of automorphisms of the field of complex numbers, and describe, in the special case of polynomials with only two critical values, Grothendieck's program of 'Dessins d' enfants', aiming at giving representations of the absolute Galois group. We describe Chebycheff and Belyi polynomials, and other explicit examples. As an illustration, we briefly treat difference and Schur polynomials. Then we concentrate on a higher dimensional analogue of the triangle curves, namely, Beauville surfaces and varieties isogenous to a product. We describe their moduli spaces, and show how the study of these varieties leads to new interesting questions in the theory of finite (simple) groups.