A remark on a conjecture of Hain and Looijenga

Faber, Carel

Annales de l'Institut Fourier, Tome 61 (2011) no. 7, pp. 2745-2750.

Nous montrons que la généralisation naturelle d’une conjecture de Hain et Looijenga au cas des courbes épointées tient pour tout $g$ et $n$ si et seulement si les anneaux tautologiques des espaces des modules des courbes à queues rationnelles et des courbes stables sont des anneaux de Gorenstein.

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.

Classification : 14H10, 13H10
Keywords: Moduli spaces of curves, tautological ring, Gorenstein ring
Mot clés : Espaces de module des courbes, anneau tautologique, anneau de Gorenstein

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