Publications of the Research Institute for Mathematical Sciences


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Volume 38, Issue 4, 2002, pp. 693–724
DOI: 10.2977/prims/1145476194

Published online: 2002-12-31

Multiplicity of Filtered Rings and Simple K3 Singularities of Multiplicity Two

Masataka Tomari[1]

(1) Kanazawa University, Japan

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) ∈ ℝ4. 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.

Keywords: Multiplicity, filtered rings, simple K3 singularity

Tomari Masataka: Multiplicity of Filtered Rings and Simple K3 Singularities of Multiplicity Two. Publ. Res. Inst. Math. Sci. 38 (2002), 693-724. doi: 10.2977/prims/1145476194