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arXiv · 2310.19610

Addition-deletion results for plus-one generated curves

Anca Măcinic·Piotr Pokora
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Abstract

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.

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Anca Măcinic, Piotr Pokora. 2023-10-30. Addition-deletion results for plus-one generated curves. https://doi.org/10.1007/s10801-024-01350-x

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