The embedded deformation problem for monomial ideals
Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel pith:SWYKBKGSrecord.jsonopen to challenge →
read the original abstract
This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$. More precisely, we establish that an embedded deformation of $R$ corresponds exactly to a degree two central element in the homotopy Lie algebra of $R$, as well as a free summand of the conormal module of $R$. A major input in the proof is an analysis of cohomological support varieties. Other main results include establishing a lower bound for the dimension of the cohomological support variety of any complex over such rings, and classifying all possible subvarieties of affine $n$-space that are the cohomological support of rings defined by $n$ monomial relations where $n$ is five or less.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
SPEARBench: A Benchmark for Naturalness Evaluation in Streaming Speech-to-Speech Language Models
An open-source benchmark for speech-to-speech models shows that current systems produce intelligible audio but diverge from human conversational behavior in latency, dialect consistency, emotional entrainment, and prosody.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.