# ANNALES DE L'INSTITUT FOURIER

Principal boundary of moduli spaces of abelian and quadratic differentials
Annales de l'Institut Fourier, Volume 69 (2019) no. 1, pp. 81-118.

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.

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.

Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3239
Classification: 14H10, 14H15, 30F30, 32G15
Keywords: Abelian differential, principal boundary, moduli space of stable curves, spin and hyperelliptic structures
Chen, Dawei 1; Chen, Qile 1

1 Department of Mathematics Boston College Chestnut Hill, MA 02467 (USA)
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Chen, Dawei; Chen, Qile. Principal boundary of moduli spaces of abelian and quadratic differentials. Annales de l'Institut Fourier, Volume 69 (2019) no. 1, pp. 81-118. doi : 10.5802/aif.3239. https://aif.centre-mersenne.org/articles/10.5802/aif.3239/

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