Cotangent spaces and separating re-embeddings

Given an affine algebra [Formula: see text], where text] is a polynomial ring over field and ideal in we study re-embeddings of the scheme i.e. presentations such that fewer indeterminates. To find re-embeddings, use polynomials which are coherently separating sense they form with indeterminate divides neither term support nor for text]. The possible numbers sets shown to be governed by Gröbner fan dimension cotangent space at text]-linear maximal lower bound embedding dimension, if corresponding this bound, know have determined found optimal re-embedding.