English

On deformations of maps and curve singularities

Algebraic Geometry 2008-05-29 v3 Commutative Algebra

Abstract

We study several deformation functors associated to the normalization of a reduced curve singularity (X,0) \subset (\c^n,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,T^i, 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\hoa{A}_e-codimension of a parametrized curve singularity, where \hoaAe\hoa{A}_e denotes the Mather-Wall group of left-right equivalence.

Keywords

Cite

@article{arxiv.0707.4290,
  title  = {On deformations of maps and curve singularities},
  author = {G. -M. Greuel and Cong Trinh Le},
  journal= {arXiv preprint arXiv:0707.4290},
  year   = {2008}
}

Comments

19 pages; few remarks, a reference, an item of a corollary added; a proposition revised. To be published in Manuscripta Mathematica 2008

R2 v1 2026-06-21T09:02:47.139Z