Multiplicity of filtered rings and simple \(K3\) singularities of multiplicity two.
Summary: Given a filtered ring, we give bounds of its multiplicity in terms of the data of the tangent cone using the technique of the filtered blowing-up. Applying it to each simple \(K3\) singularity of multiplicity two, we find a good coordinate where the Newton boundary of the defining equation contains the point \((1,1,1,1)\in\mathbb{R}^4\). In the course of the proof, we classify simple \(K3\) singularities of multiplicity two into 48 weight types. Furthermore, we prove that the weight type of the singularity stays the same under arbitrary one-parameter (FG)-deformations.
scientific article; zbMATH DE number 1902207