Newton polyhedra (resolution of singularities) (Q796590)

In the study of (algebraic) complete intersections in \(\mathbb{C}^n\) or of germs of analytic complete intersections in \((\mathbb{C}^n,0)\) a very powerful tool is the use of toric varieties, associated to the corresponding Newton polyhedra. The aim of the paper is to obtain results concerning resolutions of singularities and smooth compactifications for complete intersections as above. The results hold in particular when the coefficients of the polynomial equations (resp. analytical equations) are sufficiently general (assuming here that the Newton polyhedra are fixed). A first part of the paper contains a detailed construction of toric varieties (smooth case), involving less algebraic formalism as in the original one [cf. \textit{G. Kempf}, \textit{F. Knudsen}, \textit{D. Mumford} and \textit{B. Saint-Donat}, Toroidal embeddings. I. Berlin etc.: Springer Verlag (1973; Zbl 0271.14017)].