4 papers
math.DG2025
On vertices and inflections of singular plane curves
James William Bruce, Marco Antônio do Couto Fernandes, Farid Tari
Given the germ of a smooth plane curve , with an isolated singularity, we define two invariants a…
math.DG2024
On geometric invariants of singular plane curves
J. W. Bruce, M. A. C. Fernandes, F. Tari
Given a germ of a smooth plane curve , with an isolated singularity, we define two invariants and $V_…
math.DG2023
On the affine geometry of congruences of lines
J. W. Bruce, F. Tari
Congruences, or -parameter families of lines in -space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geom…
math.DG2023
Binary differential equations associated to congruences of lines in Euclidean 3-space
J. W. Bruce, F. Tari
We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential forms, shed some light on classic…