Freeness of conic-line arrangements in P²

Let ζ = ∪ⁿ_i=1 C_i C P² be a collection of smooth rational plane curves. We prove that the addition-deletion operation used in the study of hyperplane arrangements has an extension which works for a large class of arrangements of smooth rational curves, giving an inductive tool for understanding the freeness of the module Ω¹ (ζ) of logarithmic differential forms with pole along ζ. We also show that the analog of Terao's conjecture (freeness of Ω¹ (ζ) is combinatorially determined if ζ is a union of lines) is false in this setting.