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Winter 2021 On ideals generated by a-fold products of linear forms
Ştefan O. Tohǎneanu
J. Commut. Algebra 13(4): 549-570 (Winter 2021). DOI: 10.1216/jca.2021.13.549

Abstract

Let 𝕂 be any field. Given n linear forms in R=𝕂[x1,,xk], some possibly proportional, in one of our main results we show that the ideal IR generated by all (n2)-fold products of these linear forms has linear graded free resolution. When no two of the linear forms considered are proportional, this result helps determining a complete set of generators of the symmetric ideal of I. Via Sylvester forms we can analyze from a different perspective the generators of the presentation ideal of the Orlik–Terao algebra of the second order; this is the algebra generated by the reciprocals of the products of any two (distinct) of the linear forms considered.

Citation

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Ştefan O. Tohǎneanu. "On ideals generated by a-fold products of linear forms." J. Commut. Algebra 13 (4) 549 - 570, Winter 2021. https://doi.org/10.1216/jca.2021.13.549

Information

Received: 14 October 2018; Revised: 19 May 2019; Accepted: 24 May 2019; Published: Winter 2021
First available in Project Euclid: 18 January 2022

Digital Object Identifier: 10.1216/jca.2021.13.549

Subjects:
Primary: 13D02
Secondary: 13A30 , 14N20 , 52C35

Keywords: hyperplane arrangements , ideals generated by products of linear forms , linear free resolution , Orlik–Terao algebra , special fiber , symmetric ideal

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 4 • Winter 2021
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