Addition-deletion results for plus-one generated curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866912112412983296 |
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| author | Măcinic, Anca Pokora, Piotr |
| author_facet | Măcinic, Anca Pokora, Piotr |
| contents | In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and derive a characterisation of free curves in terms of behaviour to addition/deletion of lines. We describe the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19610 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Addition-deletion results for plus-one generated curves Măcinic, Anca Pokora, Piotr Algebraic Geometry Commutative Algebra In the recent paper A. Dimca proves that when one adds to or deletes a line from a free curve the resulting curve is either free or plus-one generated. We prove the converse statements, we give an additional insight into the original deletion result, and derive a characterisation of free curves in terms of behaviour to addition/deletion of lines. We describe the possible splitting types of the bundle of logarithmic vector fields associated to a plus-one generated curve. |
| title | Addition-deletion results for plus-one generated curves |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2310.19610 |