Observations on how adding or deleting a smooth conic affects free curves, suggesting geometric implications.
We describe the behavior of a free reduced plane projective curve with respect to the addition, respectively, deletion, of a smooth conic. These results apply in particular to conic-line arrangements. We present some obstructions to the geometry and combinatorics of a free reduced curve, generalizing results known a priori only for free projective line arrangements.
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Anca Macinic (2026) studied this question.
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