On plane conic arrangements with nodes and tacnodes
Algebraic Geometry
2022-06-01 v4 Combinatorics
Abstract
In the present paper, we study arrangements of smooth plane conics having only nodes and tacnodes as the singularities. We provide an interesting 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 turns out to be better than 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.
Cite
@article{arxiv.2108.04004,
title = {On plane conic arrangements with nodes and tacnodes},
author = {Alexandru Dimca and Marek Janasz and Piotr Pokora},
journal= {arXiv preprint arXiv:2108.04004},
year = {2022}
}
Comments
11 pages, this is the final version incorporating referee's remarks, to appear in Innovations in Incidence Geometry - Algebraic, Topological and Combinatorial