Abstract
LetC be a generically smooth, locally complete intersection curve defined over an algebraically closed fieldk of characteristicp≥0. LetG⊃ Aut k C be a finite group of automorphisms ofC. We develop a theory ofG-equivariant deformations of the Galois coverC→C/G. We give a thorough study of the local obstructions, those localized at singular or widely ramified points, to deform equivariantly a cover. As an application, we discuss the case ofG-equivariant deformations of semistable curves.
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Bertin, J., Mézard, A. Déformations formelles de revêtements: un principe local-global. Isr. J. Math. 155, 281–307 (2006). https://doi.org/10.1007/BF02773957
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DOI: https://doi.org/10.1007/BF02773957