On plane conic arrangements with nodes and tacnodes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

On plane conic arrangements with nodes and tacnodes

Alexandru Dimca
Marek Janasz
  • Fonction : Auteur
Piotr Pokora
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03531108 , version 1 (18-01-2022)

Identifiants

Citer

Alexandru Dimca, Marek Janasz, Piotr Pokora. On plane conic arrangements with nodes and tacnodes. 2022. ⟨hal-03531108⟩
14 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More