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Let ${\mathcal C}= \bigcup_{i=1}^n C_i \subseteq \mathbb{P}^2$ be acollection of smooth rational plane curves. We prove that the addition-deletionoperation used in the study of hyperplane arrangements has an extension whichworks for a large class of arrangements of smooth rational curves, giving aninductive tool for understanding the freeness of the module $\Omega^1({\mathcalC})$ of logarithmic differential forms with pole along ${\mathcal C}$. We alsoshow that the analog of Terao's conjecture (freeness of $\Omega^1({\mathcalC})$ is combinatorially determined if ${\mathcal C}$ is a union of lines) isfalse in this setting.

Freeness of Conic-Line Arrangements in $\mathbb P^2$