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

Bilal Balo

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

Algebraic Geometry 2025-12-30 v2

Authors: Bilal Balo

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 $\mathbb{C}^n$ .

Keywords

Newton nondegenerate p-form toric reduction of singularities Newton polyhedron dual fan holomorphic form singularity

Cite

@article{arxiv.2507.05430,
  title  = {Toric reduction of singularities for Newton nondegenerate $p$-forms},
  author = {Bilal Balo},
  journal= {arXiv preprint arXiv:2507.05430},
  year   = {2025}
}

Comments

14 pages, 2 figures. Addition of two new results in v2: the inverse implication for the main theorem in Section 3 and an application. Fixed typos and some minor changes in the presentation

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

Abstract

Keywords

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