Principal boundary of moduli spaces of abelian and quadratic differentials
[Limite principale des espaces de modules des différentielles abéliennes et quadratiques]
Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 81-118.

Le travail fondateur d’Eskin–Masur–Zorich a décrit la limite principale des espaces de modules des différentielles abéliennes qui paramètre les surfaces plates possédant une configuration générique de petites connexions de selles parallèles prescrite. Dans cet article, nous décrivons la limite principale pour chaque configuration en terme de différentielles entrelacées sur les courbes stables pointées de Deligne–Mumford. Nous décrivons également la limite principale des espaces de modules des différentielles quadratiques étudiée à l’origine par Masur–Zorich. Nos principaux outils sont la dégénérescence géométrique plate et le lissage développés par Bainbridge–Chen–Gendron–Grushevsky–Möller.

The seminal work of Eskin–Masur–Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe the principal boundary for each configuration in terms of twisted differentials over Deligne–Mumford pointed stable curves. We also describe similarly the principal boundary of moduli spaces of quadratic differentials originally studied by Masur–Zorich. Our main technique is the flat geometric degeneration and smoothing developed by Bainbridge–Chen–Gendron–Grushevsky–Möller.

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DOI : https://doi.org/10.5802/aif.3239
Classification : 14H10,  14H15,  30F30,  32G15
Mots clés : Différentiel abélien, limite principale, espace modulaire des courbes stables, structures spinales et hyperelliptiques
@article{AIF_2019__69_1_81_0,
     author = {Chen, Dawei and Chen, Qile},
     title = {Principal boundary of moduli spaces of abelian and quadratic differentials},
     journal = {Annales de l'Institut Fourier},
     pages = {81--118},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {69},
     number = {1},
     year = {2019},
     doi = {10.5802/aif.3239},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3239/}
}
Chen, Dawei; Chen, Qile. Principal boundary of moduli spaces of abelian and quadratic differentials. Annales de l'Institut Fourier, Tome 69 (2019) no. 1, pp. 81-118. doi : 10.5802/aif.3239. http://archive.numdam.org/articles/10.5802/aif.3239/

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