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 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 -codimension of a parametrized curve singularity, where denotes the Mather-Wall group of left-right equivalence.
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