2 research outputs found
Bitangents of real algebraic curves: signed count and constructions
We study real bitangents of real algebraic plane curves from two
perspectives. We first show that there exists a signed count of such bitangents
that only depends on the real topological type of the curve. From this follows
that a generic real algebraic curve of even degree has at least
real bitangents. Next we explain how to locate (real)
bitangents of a (real) perturbation of a multiple (real) conic in
. As main applications, we exhibit a real sextic with a total of
real bitangents and 6 complex ones, and perform asymptotical
constructions that give the best, to our knowledge, number of real bitangents
of real algebraic plane curves of a given degree.Comment: 38 pages, 22 Figures, comments welcom