2007/07/29 by Gert–Martin Greuel, G. -M. Greuel, Greuel, G. -M. +3
Mathematics · #14B05 #14B07 #14B10 #14B12 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AG #msc:14B05 #msc:14B07 #msc:14B10 #msc:14B12
paper · pdf · doi:10.48550/arxiv.0707.4290
19 pages; few remarks, a reference, an item of a corollary added; a proposition revised. To be published in Manuscripta Mathematica 2008
openalex publication_date 2007/07/29 · arxiv created 2008/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study several deformation functors associated to the normalization of a reduced curve singularity (X,0) ⊂ (\cn,0). The main new results are explicit formulas, in terms of classical invariants of (X,0), for the cotangent cohomology groups Ti, i = 0,1,2, of these functors. Thus we obtain precise statements about smoothness and dimension of the corresponding local moduli spaces. We apply the results to obtain explicit formulas resp. estimates for the \hoaAe-codimension of a parametrized curve singularity, where \hoaAe denotes the Mather-Wall group of left-right equivalence.