A homological approach for computing the tangent space of the deformation functor of curves with automorphisms

2003/12/24 by Aristides Kontogeorgis, Kontogeorgis, Aristides
Computer Science · Mathematics · #14H10 #14H37 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AG #msc:14H10 #msc:14H37

paper · pdf · doi:10.48550/arxiv.math/0312447

arxiv created 2003/12/24 · openalex publication_date 2003/12/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an alternative approach to the computation of the dimension of the tangent space of the deformation space of curves with automorphisms. A homological version of the local-global principle similar to the one of J.Bertin, A. Mézard is proved, and a computation in the case of ordinary curves is obtained, by application of the results of S. Nakajima for the Galois module structure of the space of 2-holomorphic differentials on them.

Citations

• Equivariant deformation of Mumford curves and of ordinary curves in positive characteristic

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• Polydifferentials and the deformation functor of curves with automorphisms II
• Quadratic differentials and equivariant deformation theory of curves
• On the Krull Dimension of the deformation ring of curves with automorphisms
• Deformations and automorphisms: a framework for globalizing local tangent and obstruction spaces