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À propos du théorème de Belyi

Jean-Marc Couveignes (1996)

Journal de théorie des nombres de Bordeaux

Le théorème de Belyi affirme que sur toute courbe algébrique C lisse projective et géométriquement connexe, définie sur ℚ ¯ , il existe une fonction f non ramifiée en dehors de 0 , 1 , ∞ . Nous montrons que cette fonction peut être choisie sans automorphismes, c’est-à-dire telle que pour tout automorphisme non trivial a de C , on ait f ∘ 𝔞 ≠ f . Nous en déduisons que si 𝕂 ⊂ ℂ est une extension finie de ℚ , toute 𝕂 -classe d’isomorphisme de courbes algébriques lisses projectives géométriquement connexes peut être caractérisée...

A really elementary proof of real Lüroth's theorem.

T. Recio, J. R. Sendra (1997)

Revista Matemática de la Universidad Complutense de Madrid

Classical Lüroth theorem states that every subfield K of K(t), where t is a transcendental element over K, such that K strictly contains K, must be K = K(h(t)), for some non constant element h(t) in K(t). Therefore, K is K-isomorphic to K(t). This result can be proved with elementary algebraic techniques, and therefore it is usually included in basic courses on field theory or algebraic curves. In this paper we study the validity of this result under weaker assumptions: namely, if K is a subfield...

A remark on a conjecture of Hain and Looijenga

Carel Faber (2011)

Annales de l’institut Fourier

We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all g and n if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.

A remark on the homotopical dimension of some moduli spaces of stable Riemann surfaces

Gabriele Mondello (2008)

Journal of the European Mathematical Society

Using a result of Harer, we prove certain upper bounds for the homotopical/cohomological dimension of the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. These bounds would follow from conjectures of Looijenga and Roth–Vakil.

A remark on the Picard group of spin moduli space

Maurizio Cornalba (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We describe a number of classes in the Picard group of spin moduli space and determine the relations they satisfy; as an application we show that the Picard group in question contains 4-torsion elements.

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