Zero sets and Nullstellensatz type theorems for slice regular quaternionic polynomials

2022/12/05 by Anna Maria Gori, Giulia Sarfatti, Gori, Anna +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #16S36 #30G35 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Elasticity and Wave Propagation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2212.02301

openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the vanishing sets of slice regular polynomials in several quaternionic variables. We obtain a geometric description of the vanishing sets in two variables, which leads to a new version of the Strong Hilbert Nullstellensatz in the quaternionic setting.

Cited by

• Division algebras of slice-Nash functions
• On the irreducibility of slice algebraic sets

Related

• A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
• Resultants of slice regular polynomials in two quaternionic variables
• On the geometry of zero sets of central quaternionic polynomials
• Zeroes of weakly slice regular functions of several quaternionic variables on non-axially symmetric domains
• Matrix versions of real and quaternionic nullstellensatz