Classification of 3-dimensional isolated rational hypersurface singularities with C*-action

TL;DR

This paper classifies 3-dimensional isolated rational hypersurface singularities with C*-action, providing a comprehensive list crucial for understanding algebraic structures related to CR manifolds and their links to topological spheres.

Contribution

It offers a complete classification list of 3D rational hypersurface singularities with C*-action, filling a gap in existing mathematical literature.

Findings

Classification list of singularities is provided

Links between singularities and CR structures are clarified

Supports algebraic and topological analysis of CR manifolds

Abstract

In the paper "Algebraic classification of rational CR structures on topological 5-sphere with transversal holomorphic S^1-action in C^4" (Yau and Yu, Math. Nachrichten 246-247(2002), 207-233), we give algebraic classification of rational CR structures on the topological 5-sphere with transversal holomorphic S^1-action in C^4. Here, algebraic classification of compact strongly pseudoconvex CR manifolds X means classification up to algebraic equivalence, i.e. roughly up to isomorphism of the normalization of the complex analytic variety V which has X as boundary. The problem is intimately related to the study of 3-dimensional isolated rational weighted homogeneous hypersurface singularities with link homeomorphic to S^5. For this, we need the classification of 3-dimensional isolated rational hypersurface singularities with a C*-action. This list is only available at the homepage of one of us. Since there is a desire for a complete list of this classification (cf. Theorem 3.3), we decide to publish it for the convenience of readers.