Generalized Newton complementary duals of monomial ideals

Katie Ansaldi; Kuei Nuan Lin; Yi Huang Shen

doi:10.1142/S0219498821500213

Generalized Newton complementary duals of monomial ideals

Katie Ansaldi, Kuei Nuan Lin, Yi Huang Shen

Penn State Greater Allegheny

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	2150021
Journal	Journal of Algebra and its Applications
Volume	20
Issue number	2
DOIs	https://doi.org/10.1142/S0219498821500213
State	Published - Feb 2021

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498821500213

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title = "Generalized Newton complementary duals of monomial ideals",

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. ",

author = "Katie Ansaldi and Lin, {Kuei Nuan} and Shen, {Yi Huang}",

note = "Funding Information: The authors thank Alberto Corso for sharing his experiments which inspires this work. The authors thank Claudia Polini and Sonja Mapes for useful discussions and careful readings of the paper. They also want to express heartfelt thanks to the reviewer for the suggestions that greatly improved this paper. The third author is partially supported by the “Fundamental Research Funds for the Central Universities”. Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

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N1 - Funding Information: The authors thank Alberto Corso for sharing his experiments which inspires this work. The authors thank Claudia Polini and Sonja Mapes for useful discussions and careful readings of the paper. They also want to express heartfelt thanks to the reviewer for the suggestions that greatly improved this paper. The third author is partially supported by the “Fundamental Research Funds for the Central Universities”. Publisher Copyright: © 2021 World Scientific Publishing Company.

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N2 - 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.

AB - 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.

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Generalized Newton complementary duals of monomial ideals

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