Freeness of hyperplane arrangements with cubic minimal logarithmic derivations

Junyan Chu and Guangfeng Jiang – GJM, Volume 8, Issue 2 (2023), 88-106.

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• février 9, 2024
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A line arrangement is a finite set of affine lines in the projective plane. Despite its apparent simplicity, it unveils a diverse array of algebraic and combinatorial phenomena. Among the algebraic invariants of line arrangements, the module of logarithmic derivations, which consists of polynomial vector fields tangent to the lines, has played a central role. In this paper, we study the properties of this module based on algorithmic and combinatorial techniques. The primary focus is on the minimal generators of the module and its freeness. In particular, we give a complete determination of the minimal module generators for a specific class of free line arrangements, namely, those with a minimal logarithmic derivation of degree three.

Milestones:

Received: February 06, 2023
Accepted: December 30, 2023
Revised: January 6, 2024

Authors:

Junyan Chu
Graduate School of Mathematics,
Kyushu University, Japan.
Guangfeng Jiang
Mathematical Institute, Beijing University of Chemical Technology,
Beijing, 100029, China.

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