Computing the Topology of an Arrangement of Quartics

摘要

We analyze how to compute in an efficient way the topology of an arrangement of quartic curves. We suggest a sweeping method that generalizes the one presented by Eigenwillig et al. for cubics. The proposed method avoids working with the roots of the involved resultants (most likely algebraic numbers) in order to give an exact and complete answer. We only treat in detail the cases of one and two curves because we do not introduce any significant variation in the several curves case with respect to Eigenwillig’s paper.