Fiber polytopes and fractional power series Original Research Article

This paper explores the power series expansions of polynomial equations in N variables. Expansions considered have exponents lying in some convex conical region in RN. An N-variable analog of the Newton polygon construction for polynomials in two variables is used to construct such series expansions. The structure of these series is related to the theory of fiber polytopes as introduced by Billera and Sturmfels in [2], and this relationship is used to draw conclusions about certain ramification loci.