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On plane conic
arrangements with nodes and tacnodes
Alexandru Dimca, Marek Janasz and Piotr Pokora |
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Vol. 19 (2022), No. 2, 47–58
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Abstract |
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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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Keywords
conic arrangements, nodes, tacnodes, freeness, nearly
freeness
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Mathematical Subject Classification
Primary: 14N20
Secondary: 14C20, 32S22
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Milestones
Received: 20 October 2021
Accepted: 29 January 2022
Published: 28 May 2022
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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 |
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| Piotr Pokora | |
| Department of Mathematics Pedagogical University of Krakow 30-084 Kraków Poland |
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