NEWTON'S POLYHEDRA AND REDUCED SYSTEMS

This paper discusses a geometric-analytic method for investigating the structure of solution branches to systems of algebraic equations in a neighborhood of a singular point. The method is based on the Newton polyhedron and the construction of reduced systems. Historical developments, from Sintsov's graphical technique to Bruno’s power geometry framework, are reviewed. A novel method is proposed for calculating the leading terms and separation of branches using cones of reductions and Newton diagrams.