Versal deformations of pairs and Cohen-Macaulay approximation
Abstract
For a pair (algebra, module) with equidimensional and isolated singularity we establish the existence of a versal henselian deformation. Obstruction theory in terms of an Andr\'e-Quillen cohomology for pairs is a central ingredient in the Artin theory used. In particular we give a long exact sequence relating the algebra cohomology and the module cohomology with the cohomology of the pair and define a Kodaira-Spencer class for pairs. Cohen-Macaulay approximation induces maps between versal base spaces for pairs and cohomology conditions imply properties like smoothness, isomorphism and linear section.
Keywords
Cite
@article{arxiv.1907.08970,
title = {Versal deformations of pairs and Cohen-Macaulay approximation},
author = {Runar Ile},
journal= {arXiv preprint arXiv:1907.08970},
year = {2021}
}
Comments
v3, 30 pages. Sections 3, 8 and 9 are new. Some changes and additions to the other sections. References have been added and the introduction expanded. This preprint supersedes parts of sections 8, 10 and 12 in arXiv: 1103.2712