Research ArticleNo Access

Generalized Newton complementary duals of monomial ideals

Katie Ansaldi

https://orcid.org/0000-0002-6366-4571

Department of Mathematics and Computer Science, Wabash College, Crawfordsville, IN, USA

E-mail Address: ansaldik@wabash.edu

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Kuei-Nuan Lin

https://orcid.org/0000-0002-3320-6246

Department of Mathematics, Penn State Greater Allegheny, McKeesport, PA, USA

E-mail Address: kul20@psu.edu

Corresponding author.

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Yi-Huang Shen

Wu Wen-Tsun Key Laboratory of Mathematics of CAS, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China

E-mail Address: yhshen@ustc.edu.cn

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https://doi.org/10.1142/S0219498821500213Cited by:0 (Source: Crossref)

Abstract

Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphism between the special fiber rings. We construct the cellular free resolutions of duals of strongly stable ideals generated in the same degree. When the base ideal is generated in degree two, we provide an explicit description of cellular free resolution of the dual of a compatible generalized stable ideal.

Communicated by T. H. Ha

Keywords:

AMSC: 13D02, 05E40

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