On the construction of valuations and generating sequences on hypersurface singularities

Suppose that (K, ν) is a valued field, f (z) ∈ K[z] unitary and irreducible polynomial (L, ω) an extension of fields, where L = K[z]/(f (z)). Further suppose A local domain with quotient field K such ν has nonnegative value on positive its maximal ideal, in A[z]. This paper devoted to the problem describing structure associated graded ring gr ω A[z]/(f (z)) for filtration defined by as ν. In particular we give algorithm which many cases produces finite set elements whose images generate it A-algebra well relations between them. We also work out interactions our method computation phenomena complicate study ramification uniformization characteristic , non tameness defect extension. For valuations rank one separable fields ⊂ above generating sequence birational A1 dominated if only there no defect. this case, A1[z]/(f finitely presented A1-module. improved version, thanks referee's remarks.