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Equivariant deformations of semi-stable curves. (Déformations équivariantes des courbes semistables.) (French) Zbl 1095.14022

Let \(K\) be an algebraically closed field of characteristic \(p\). The paper under review discusses the (equivariant) deformation theory of a Galois cover of curve \(f: X \rightarrow Y\), where \(X\) has one ordinary double point. Let \(G\) be the Galois group of the cover \(f\). In the first part of the paper, the authors identify several local obstructions to lift the action of \(G\) to a versal deformation of \(X\). In the second part the global obstructions are studied. One of the results is that, contrary to the smooth case, there exist global obstructions that cannot be reduced to local obstructions.

MSC:

14H10 Families, moduli of curves (algebraic)
14B10 Infinitesimal methods in algebraic geometry
14H30 Coverings of curves, fundamental group
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