4 papers
Blurred combinatorics in resolution of singularities: (a little) beyond the characteristic polytope
Helena Cobo, M. J. Soto, José M. Tornero
We introduce a variation of the well-known Newton-Hironaka polytope for algebroid hypersurfaces. This combinatorial object is a perturbed version of the original one, parametrized…
Combinatorics and their evolution in resolution of embedded algebroid surfaces
Helena Cobo, M. J. Soto, José M. Tornero
The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracki…
The Newton Procedure for several variables
M. J. Soto, J. L. Vicente
We show that the roots of a Weierstrass polynomial on several variables are power series with rational exponents of bounded denominators, whose Newton diagrams are contained in an…
Pyramids and monomial blowing-ups
M. J. Soto, José L. Vicente
We show that a convex pyramid in R^n with apex at 0 can be brought to the first quadrant by a finite sequence of monomial blowing-ups if and only if its intersection with the oppos…