Perturbation of quadrics Original Research Article

The aim of this paper is to study what happens when a slight perturbation affects the coefficients of a quadratic equation defining a variety (a quadric) in image . Structurally stable quadrics are those such that a small perturbation on the coefficients of the equation defining them does not give rise to a “different” (in some sense) set of points. In particular, we characterize structurally stable quadrics and give the “bifurcation diagrams” of the non-stable ones (showing which quadrics meet all of their neighbourhoods), when dealing with the “affine” and “metric” equivalence relations. This study can be applied to the case where a set of points, which constitute the set of solutions of a problem, is defined by a quadratic equation whose coefficients are given with parameter uncertainty.