Differential modules and Deformations of Free Complexes
Commutative Algebra
2023-08-07 v1 Algebraic Geometry
Abstract
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to parameterize the deformations and obstructions in terms of certain Ext groups, giving an algorithmic realization of a result of Brown-Erman. We apply this theory to study certain rigidity properties of free resolutions and related rank conjectures.
Cite
@article{arxiv.2308.01973,
title = {Differential modules and Deformations of Free Complexes},
author = {Maya Banks and Keller VandeBogert},
journal= {arXiv preprint arXiv:2308.01973},
year = {2023}
}
Comments
18 pages