Vol. 19, No. 2, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Volume 19, Issue 1
Volume 18, Issue 1
Volume 17, Issue 3
Volume 17, Issue 2
Volume 17, Issue 1
Volume 16, Issue 1
Volume 15, Issue 1
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 1
Volume 10, Issue 1
Volume 9, Issue 1
Volume 8, Issue 1
Volume 6+7, Issue 1
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
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
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