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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.01212 |
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| _version_ | 1866910568517992448 |
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| author | Chu, Junyan |
| author_facet | Chu, Junyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free resolution of the logarithmic derivation modules of close to free arrangements Chu, Junyan Commutative Algebra Algebraic Geometry Combinatorics 52C35, 14N20 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. |
| title | Free resolution of the logarithmic derivation modules of close to free arrangements |
| topic | Commutative Algebra Algebraic Geometry Combinatorics 52C35, 14N20 |
| url | https://arxiv.org/abs/2401.01212 |