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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avramov, L.L.: A cohomological study of local rings of embedding codepth 3. J. Pure Appl. Algebra 216(11), 2489–2506 (2012). MR2927181
Avramov, L.L., Kustin, A.R., Miller, M.: Poincaré series of modules over local rings of small embedding codepth or small linking number. J. Algebra 118(1), 162–204 (1988). MR0961334
Brown, A.E.: A structure theorem for a class of grade three perfect ideals. J. Algebra 105(2), 308–327 (1987). MR0873666
Buchsbaum, D.A., Eisenbud, D.: Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3. Am. J. Math. 99(3), 447–485 (1977). MR0453723
Grayson, D.R., Stillman, M.E.: Macaulay 2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/
Watanabe, J.: A note on Gorenstein rings of embedding codimension three. Nagoya Math. J. 50, 227–232 (1973). MR0319985
Weyman, J.: On the structure of free resolutions of length 3. J. Algebra 126(1), 1–33 (1989). MR1023284
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was partly supported by NSA grant H98230-11-0214 (L.W.C.).
Rights and permissions
About this article
Cite this article
Christensen, L.W., Veliche, O. Local Rings of Embedding Codepth 3. Examples. Algebr Represent Theor 17, 121–135 (2014). https://doi.org/10.1007/s10468-012-9390-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10468-012-9390-y