On the tangent space of the deformation functor of curves with automorphisms

Details On the tangent space of the deformation functor of curves with automorphisms On the tangent space of the deformation functor of curves with automorphisms

2002-01-21

arxiv.org/abs/math/0201194v4

Mathematics

Algebraic Geometry

33 pages, A gap in the proof of lemma 1.5 is filled

Scientific paper

We provide a method to compute the dimension of the tangent space to the
global infinitesimal deformation functor of a curve together with a subgroup of
the group of automorphisms. The computational techniques we developed are
applied to several examples including Fermat curves, $p$-cyclic covers of the
affine line and to Lehr-Matignon curves.

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