Infinitesimal deformation of Galois covering space and its application to Galois closure curves (Q1428980)

The author develops a general framework for infinitesimal deformations of finite Galois covering spaces of complex dimension \(1\). He applies this framework to the case of the Galois closure of a branched covering \(Y \to X\). More precisely he computes the Kodaira-Spencer map of the corresponding family of curves parametrized by the space of morphisms from \(Y\) to \(X\) of fixed degree, showing that it is injective when the covering has only simple branching.