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Proceedings of the American Mathematical Society

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Edge rings with $ 3$-linear resolutions


Authors: Takayuki Hibi, Kazunori Matsuda and Akiyoshi Tsuchiya
Journal: Proc. Amer. Math. Soc. 147 (2019), 3225-3232
MSC (2010): Primary 05E40, 13H10, 52B20
DOI: https://doi.org/10.1090/proc/14382
Published electronically: May 8, 2019
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Abstract: It is shown that the edge ring of a finite connected simple graph with a $ 3$-linear resolution is a hypersurface.


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Additional Information

Takayuki Hibi
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
Email: hibi@math.sci.osaka-u.ac.jp

Kazunori Matsuda
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
Address at time of publication: Kazunori Matsuda, Kitami Institute of Technology, Kitami, Hokkaido 090-8507, Japan
Email: kaz-matsuda@mail.kitami-it.ac.jp

Akiyoshi Tsuchiya
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
Email: a-tsuchiya@ist.osaka-u.ac.jp

DOI: https://doi.org/10.1090/proc/14382
Keywords: Finite graph, edge ring, linear resolution, $\delta$-polynomial
Received by editor(s): December 18, 2017
Received by editor(s) in revised form: August 8, 2018
Published electronically: May 8, 2019
Additional Notes: The authors were partially supported by JSPS KAKENHI 26220701, 17K14165, and 16J01549.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society