Arnold’s Piecewise Linear Filtrations, Analogues of Stanley–Reisner Rings and Simplicial Newton Polyhedra

In 1974, the author proved that codimension of ideal (g1,g2,…,gd) generated in group algebra K[Zd] over a field K characteristic 0 by generic Laurent polynomials having same Newton polytope Γ is equal to d!×Volume(Γ). Assuming Newtons simplicial and super-convenient (that is, containing some neighborhood origin), strengthens 1974 result explicitly specifying set Bsh monomials cardinality d!×Volume(Γ), whose equivalence classes form basis quotient K[Zd]/(g1,g2,…,gd). The constructed inductively from any shelling sh Γ. Using structure, we prove associated graded -algebra grΓ(K[Zd]) Arnold–Newton filtration has Cohen–Macaulay property. This proof generalization B. Kind P. Kleinschmitt’s 1979 Stanley–Reisner rings complexes admitting are Cohen–Macaulay. Finally, for (f1,f2,…,fd) with Γ, defines monomial