On $\delta_m$ constant locus of versal deformations of nondegenerate hypersurface simple K3 singularities

Abstract

Hypersurface simple K3 singularities defined by nondegenerate quasi-homogeneous polynomials are classified into ninety five classes in term of the weight of the polynomial by T. Yonemura. We consider versal deformations of them. It has been conjectured that the stratum $\mu$ =const of the versal deformation of any nondegenerate hypersurface simple K3 singularity is equivalent to the $\delta_m$ constant locus. It holds true for the case deformations are also nondegenerate by K. Watanabe. On the other hand, it follows from Reid that the $\delta_m$ constant locus includes the $\mu$ constant locus generally. We show the conjecture holds true in general for No.10-14, 46-51 and 83 in the table of Yonemura.