A new hierarchy for complex plane curves
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912707898245120 |
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| author | Abe, Takuro Dimca, Alexandru Pokora, Piotr |
| author_facet | Abe, Takuro Dimca, Alexandru Pokora, Piotr |
| contents | We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Curves of type $0$ are precisely the free curves, while curves of type $1$ are the plus-one generated curves. In this paper, we first show that line arrangements and conic-line arrangements can exhibit all the theoretically possible types. In the second part, we study the properties of the curves of type $2$ and construct families of line arrangements and conic-line arrangements of this type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new hierarchy for complex plane curves Abe, Takuro Dimca, Alexandru Pokora, Piotr Algebraic Geometry Commutative Algebra Primary: 14H50, Secondary: 14B05, 13D02, 32S22 We define the type of a plane curve as the initial degree of the corresponding Bourbaki ideal. Then we show that this invariant behaves well with respect to the union of curves. Curves of type $0$ are precisely the free curves, while curves of type $1$ are the plus-one generated curves. In this paper, we first show that line arrangements and conic-line arrangements can exhibit all the theoretically possible types. In the second part, we study the properties of the curves of type $2$ and construct families of line arrangements and conic-line arrangements of this type. |
| title | A new hierarchy for complex plane curves |
| topic | Algebraic Geometry Commutative Algebra Primary: 14H50, Secondary: 14B05, 13D02, 32S22 |
| url | https://arxiv.org/abs/2410.11479 |