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The family of perfect ideals of codimension 3, of type 2 with 5 generators


Authors: Ela Celikbas, Jai Laxmi, Witold Kraśkiewicz and Jerzy Weyman
Journal: Proc. Amer. Math. Soc. 148 (2020), 2745-2755
MSC (2010): Primary 13C40, 13D02, 13H10, 15A75
DOI: https://doi.org/10.1090/proc/14646
Published electronically: March 30, 2020
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Abstract: In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the $ \operatorname {Tor}$ algebra. This family is likely to play a key role in classifying perfect ideals with five generators of type two.


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Additional Information

Ela Celikbas
Affiliation: Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506
Email: ela.celikbas@math.wvu.edu

Jai Laxmi
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: jai.laxmi@uconn.edu

Witold Kraśkiewicz
Affiliation: Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Toruń, Poland
Email: wkras@mat.umk.pl

Jerzy Weyman
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: jerzy.weyman@uconn.edu

DOI: https://doi.org/10.1090/proc/14646
Keywords: Perfect ideal, codimension three, linkage class, generic ring, Cohen-Macaulay, complete intersection
Received by editor(s): December 30, 2018
Received by editor(s) in revised form: March 1, 2019
Published electronically: March 30, 2020
Additional Notes: The first and second authors acknowledge the support of the fourth author for their visit to the University of Connecticut in Fall 2017, which was funded by the Sidney Professorial Fund.
The second author was supported by a Fulbright-Nehru fellowship
The fourth author was supported in part by the Sidney Professorial Fund and the NSF grant DMS-1802067.
Communicated by: Claudia Polini
Article copyright: © Copyright 2020 American Mathematical Society