On the geometry of zero sets of central quaternionic polynomials

2024/02/02 by Gil Alon, Alon, Gil, Elad Paran +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2402.01378

openalex publication_date 2024/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be the ring of polynomials in n central variables over the real quaternion algebra H, and let I be a left ideal in R. We prove that if a polynomial p in R vanishes at all the common zeros of I in Hⁿ with commuting coordinates, then as a slice regular quaternionic function, p vanishes at all common zeros of I in Hⁿ. This confirms a conjecture of Gori, Sarfatti and Vlacci, who settled the two dimensional case.

Cited by

• On the irreducibility of slice algebraic sets

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• A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables