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arXiv · 2401.01212

Free resolution of the logarithmic derivation modules of close to free arrangements

Junyan Chu
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Abstract

This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation module of $A$, which can be used to compute a lower bound for the graded Betti numbers of the resolution. Specifically, for the three-dimensional case, we determine the minimal free resolution of the logarithmic derivation module of $A$. We present illustrative examples of our main theorems to provide insights into the relationship between algebraic and combinatorial properties for close-to-free arrangements.

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Junyan Chu. 2024-01-02. Free resolution of the logarithmic derivation modules of close to free arrangements. https://arxiv.org/abs/2401.01212

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