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
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.

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