Abstract

Given an ideal I ⊂ RBRETx 1,…,x m, yBRET and f ∈ RBRETx 1,…, x m, yBRET , we study the subset BRETP · f ¦∂ y(P) ∈ I BRET. This idea comes from the classification of singularities of illuminated surfaces. We prove a (Hironaka-type) division theorem for subsets of this form and give a Buchberger-like reduction algorithm.

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