Associated Graded Rings and Connected Sums
Commutative Algebra
2017-05-04 v1
Abstract
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincare series of Q.
Keywords
Cite
@article{arxiv.1705.01413,
title = {Associated Graded Rings and Connected Sums},
author = {H. Ananthnarayan and Ela Celikbas and Jai Laxmi and Zheng Yang},
journal= {arXiv preprint arXiv:1705.01413},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1406.7600