On the Zariski multiplicity conjecture for weighted homogeneous and Newton non-degenerate line singularities

TL;DR

This paper introduces new classes of weighted homogeneous and Newton non-degenerate line singularities that support the Zariski multiplicity conjecture, advancing understanding in algebraic geometry.

Contribution

It provides novel examples of singularities satisfying the Zariski multiplicity conjecture, expanding the known cases and methods in the field.

Findings

New families of singularities confirmed to satisfy the Zariski multiplicity conjecture

Extension of the conjecture's validity to broader classes of singularities

Enhanced understanding of the structure of line singularities in algebraic geometry

Abstract

We present new families of weighted homogeneous and Newton non-degenerate line singularities that satisfy the Zariski multiplicity conjecture.