Notes on trimodal singularities (Q1963827)

The aim of the paper is to study surface singularities in \(\mathbb{C}^3\) of modality 3. It is proved that in suitable coordinates their equations are nondegenerate with respect to the Newton polyhedron (with a slight modification of the ``usual'' non-degeneracy). Furthermore, regular bases (in the sense of Arnold) are computed as a basis for a precise classification of the trimodal singularities with respect to \(R\)-equivalence and \(K\)-equivalence.