Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Grulha Jr., N. G., Pissolato, J. V., Ruas, M. A. S.
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910228835991552
author Grulha Jr., N. G.
Pissolato, J. V.
Ruas, M. A. S.
author_facet Grulha Jr., N. G.
Pissolato, J. V.
Ruas, M. A. S.
contents We make a detailed investigation of the generic properties that polynomial mappings possess. An important starting point is the work by Farnik, Jelonek and Ruas in 2019, where they prove some of those properties in the context of homogeneous polynomial mappings of $\mathbb{C}^3$ to $\mathbb{C}^3$, and conclude the genericity of $\mathcal{A}$-finite determinacy by applying the geometric criterion. Using their strategy, we further extend and generalize some of their key findings to dimensions greater than or equal to $2$, though some of those properties can only be extended up to dimension $4$.
format Preprint
id arxiv_https___arxiv_org_abs_2605_17350
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings
Grulha Jr., N. G.
Pissolato, J. V.
Ruas, M. A. S.
Algebraic Geometry
32S20 (Primary), 58K15 (Secondary)
We make a detailed investigation of the generic properties that polynomial mappings possess. An important starting point is the work by Farnik, Jelonek and Ruas in 2019, where they prove some of those properties in the context of homogeneous polynomial mappings of $\mathbb{C}^3$ to $\mathbb{C}^3$, and conclude the genericity of $\mathcal{A}$-finite determinacy by applying the geometric criterion. Using their strategy, we further extend and generalize some of their key findings to dimensions greater than or equal to $2$, though some of those properties can only be extended up to dimension $4$.
title Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings
topic Algebraic Geometry
32S20 (Primary), 58K15 (Secondary)
url https://arxiv.org/abs/2605.17350