CR singularities of real fourfolds in $\mathbb{C}^3$

TL;DR

This paper classifies CR singularities of real four-dimensional submanifolds in complex three-space using local coordinate transformations to understand their structure and global enumerative properties.

Contribution

It introduces a normal form classification for quadratic coefficients of CR singularities, linking local geometry to global enumerative formulas.

Findings

Normal form classification of CR singularities

Intersection index determines global enumerative formulas

Local holomorphic coordinate changes simplify analysis

Abstract

CR singularities of real 4-submanifolds in complex 3-space are classified by using local holomorphic coordinate changes to transform the quadratic coefficients of the real analytic defining equation into a normal form. The quadratic coefficients determine an intersection index, which appears in global enumerative formulas for CR singularities of compact submanifolds.