Local rings of embedding codepth 3. Examples
Lars Winther Christensen, Oana Veliche
TL;DR
This paper explores the structure of complete local rings with embedding codepth 3, providing examples that challenge existing conjectures about their algebraic structures.
Contribution
It offers new examples of algebra structures on minimal free resolutions that were previously conjectured not to exist.
Findings
Examples of algebra structures with embedding codepth 3
Counterexamples to existing conjectures
Insights into differential graded algebra structures
Abstract
A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a differential graded algebra structure, based on which one can classify local rings of embedding codepth 3. We give examples of algebra structures that have been conjectured not to occur.
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