Vol. 19, No. 2, 2022

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On plane conic arrangements with nodes and tacnodes

Alexandru Dimca, Marek Janasz and Piotr Pokora

Vol. 19 (2022), No. 2, 47–58
DOI: 10.2140/iig.2022.19.47

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.

conic arrangements, nodes, tacnodes, freeness, nearly freeness
Mathematical Subject Classification
Primary: 14N20
Secondary: 14C20, 32S22
Received: 20 October 2021
Accepted: 29 January 2022
Published: 28 May 2022
Alexandru Dimca
Université Côte d’Azur
06100 Nice
Simion Stoilow Institute of Mathematics
RO-014700 Bucharest
Marek Janasz
Department of Mathematics
Pedagogical University of Krakow
30-084 Kraków
Piotr Pokora
Department of Mathematics
Pedagogical University of Krakow
30-084 Kraków