We discuss the algebraic geometry of certain finite energy, static field configurations of an SU(N) Yang - Mills - Higgs theory in the limit of a massless scalar field and how it may be applied to their construction. We develop a systematic way of locating solutions with spherical or cylindrical symmetries. Consideration of the fields' regularity is extended from SU(2) to SU(3) as also is the description of the general monopole configuration.