Chebycheff and Belyi Polynomials, Dessins d’Enfants, Beauville Surfaces and Group Theory

By Ingrid Bauer, F. Catanese, Fritz Grunewald. 2006

61 citations recorded by the source corpus.

Abstract.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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8e9ea5a310b5e9a5d67c27a1dce9aaa0fcd72239

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In Algebra and Number Theory

1. Gunter Malle
2. Robert M. Guralnick

In Geometry and Topology

1. Robert M. Guralnick
2. Gunter Malle
3. Britta Spath
4. Pham Huu Tiep
5. M. Cabanes
6. Britta Spaeth

In Mathematical Physics

1. Robert M. Guralnick
2. Gunter Malle
3. Pham Huu Tiep
4. Britta Spath
5. Gabriel Navarro

Citations in the corpus

• Products of conjugacy classes and fixed point spaces (2010, methodology): “We also show how our methods can be used to answer a conjecture of Bauer–Catanese– Grunewald [2, 3] regarding Beauville structures (this is related to the existence of certain free actions of a finite group acting on a product of two smooth projective curves – see [16] for background).”