Toric reduction of singularities for Newton nondegenerate $p$-forms

TL;DR

This paper characterizes Newton nondegenerate holomorphic p-forms using toric reduction of singularities, providing insights into their structure and applications to singularities of (n-1)-forms in complex n-space.

Contribution

It introduces a new characterization of Newton nondegenerate p-forms via toric reduction, linking polyhedral geometry with singularity analysis.

Findings

Characterization of NND p-forms through toric reduction

Application to singularities of (n-1)-forms in complex space

Use of regular refinement of dual fan for singularity analysis

Abstract

We study a class of holomorphic $p$-forms satisfying nondegeneracy conditions expressed through their Newton polyhedron and called Newton nondegenerate (NND). We give a characterization of NND $p$-forms by their toric reduction of singularities defined through a regular refinement of their dual fan. We then present an application of this result to the study of singularities of $(n-1)$-forms on $\mathbb{C}^n$.