Equations, inequations and inequalities characterizing the configurations of two real projective conics
Abstract
Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well--adapted to the study of the relative position of two conics defined by equations depending on parameters.
Cite
@article{arxiv.math/0505628,
title = {Equations, inequations and inequalities characterizing the configurations of two real projective conics},
author = {Emmanuel Briand},
journal= {arXiv preprint arXiv:math/0505628},
year = {2025}
}
Comments
31 pages. Related material at http://emmanuel.jean.briand.free.fr/publications/twoconics/. Version 2: Added references to important prior work on the subject. The title changed accordingly. Some typos and imprecisions corrected. Version 3: fix image formats that were not compatible anymore with compiling on arxiv. See errata at http://emmanuel.jean.briand.free.fr/publications/twoconics/errata.pdf