Addition-deletion for conic-line arrangements with split Chern polynomial
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911190645473280 |
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| author | Măcinic, Anca Vallès, Jean |
| author_facet | Măcinic, Anca Vallès, Jean |
| contents | We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the same time similar results on projective lines arrangements whose characteristic polynomial factors over the integers and results on free curves. We give a splitting criterion for a rank 2 vector bundle, in terms of restrictions to smooth conics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Addition-deletion for conic-line arrangements with split Chern polynomial Măcinic, Anca Vallès, Jean Algebraic Geometry 14H50 (Primary), 14B05, 14F06, 14H60, 14C17, 32S22 (Secondary) We present combinatorial/geometric obstructions induced by the factorization over the integers of the Chern polynomial of the bundle of logarithmic vector fields associated to a complex projective plane curve. Our results generalize at the same time similar results on projective lines arrangements whose characteristic polynomial factors over the integers and results on free curves. We give a splitting criterion for a rank 2 vector bundle, in terms of restrictions to smooth conics. |
| title | Addition-deletion for conic-line arrangements with split Chern polynomial |
| topic | Algebraic Geometry 14H50 (Primary), 14B05, 14F06, 14H60, 14C17, 32S22 (Secondary) |
| url | https://arxiv.org/abs/2510.02771 |