Holomorphic maps between moduli spaces

Antonakoudis, Stergios; Aramayona, Javier; Souto, Juan

Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 217-228.

Nous démontrons que toute application non-constante et holomorphe ${ℳ}_{g,p}\to {ℳ}_{g^{\text{'}},p^{\text{'}}}$ entre deux espaces de modules est une application d’oubli, à condition que $g\ge 6$ et $g^{\text{'}}\le 2g-2$.

We prove that every non-constant holomorphic map ${ℳ}_{g,p}\to {ℳ}_{g^{\text{'}},p^{\text{'}}}$ between moduli spaces of Riemann surfaces is a forgetful map, provided that $g\ge 6$ and $g^{\text{'}}\le 2g-2$.

Classification : 57M50, 32H02
Keywords: Moduli spaces, holomorphic map, forgetful map
Mot clés : Espaces de modules, application holomorphe, application d’oubli

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