Abstract

We study arrangements of smooth plane conics having only nodes and tacnodes as singularities. We provide an estimation on the number of nodes and tacnodes that depends only on a linear function of the number of conics. Based on that result, we obtain a new upper bound on the number of tacnodes which improves on Miyaoka’s bound for a large enough number of conics. We also study the freeness and nearly freeness of such arrangements, providing a detailed description.

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