Associated Graded Rings and Connected Sums

被引：2

作者：

Ananthnarayan, H. ^{[1
]}

Celikbas, Ela ^{[2
]}

Laxmi, Jai ^{[3
]}

Yang, Zheng ^{[4
]}

机构：

[1] Indian Inst Technol, Dept Math, Main Gate Rd, Mumbai 400076, Maharashtra, India

[2] West Virginia Univ, Dept Math, 94 Beechurst Ave, Morgantown, WV 26505 USA

[3] Univ Connecticut, 341 Mansfield Rd U1009, Storrs, CT 06269 USA

[4] Sichuan Univ, Pittsburgh Inst, Jiangan Campus,Chuanda Rd, Chengdu 610207, Shuangliu Count, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2020年 / 70卷 / 01期

关键词：

associated graded ring; fibre product; connected sum; short Gorenstein ring; stretched Gorenstein ring; Poincare series; GORENSTEIN LOCAL-RINGS; POINCARE-SERIES;

D O I：

10.21136/CMJ.2019.0259-18

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：261 / 279

页数：19

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