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arXiv · 2410.11479

A new hierarchy for complex plane curves

Takuro Abe·Alexandru Dimca·Piotr Pokora
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Abstract

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.

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Takuro Abe, Alexandru Dimca, Piotr Pokora. 2025-11-05. A new hierarchy for complex plane curves. https://doi.org/10.4153/s0008439525101422

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