On the existence of tangential holomorphic vector fields vanishing at an infinite type point

TL;DR

This paper investigates the existence and properties of holomorphic vector fields tangent to real hypersurfaces in complex two-dimensional space, specifically those vanishing at points of infinite type.

Contribution

It provides new insights into the conditions under which such vector fields exist at infinite type points on real hypersurfaces.

Findings

Characterization of tangent holomorphic vector fields at infinite type points

Conditions for the existence of such vector fields

Implications for the geometry of real hypersurfaces

Abstract

The purpose of this article is to investigate the holomorphic vector fields tangent to a real hypersurface in $\mathbb C^2$ vanishing at an infinite type point.