Addition-deletion for conic-line arrangements with split Chern polynomial

Anca Măcinic; Jean Vallès

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arXiv · 2510.02771

Addition-deletion for conic-line arrangements with split Chern polynomial

Anca Măcinic·Jean Vallès

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Abstract

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.

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BibTeX RIS

Anca Măcinic, Jean Vallès. 2025-10-03. Addition-deletion for conic-line arrangements with split Chern polynomial. https://arxiv.org/abs/2510.02771

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