Computation of Hypersurface Arrangements

Hauenstein and collaborators recently introduced a numerical algorithm to identify the connected components in an arrangement of real hypersurfaces. We explain the main ideas, which are based on Morse theory, and we present novel refinements, using the likelihood equations. We offer an implementation in Julia, and we discuss an ongoing case study for arrangements of Schubert divisors in the Grassmannian of lines in 3-space.