On the geometry of zero sets of central quaternionic polynomials
Rings and Algebras
2024-02-05 v1 Algebraic Geometry
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 H^n with commuting coordinates, then as a slice regular quaternionic function, p vanishes at all common zeros of I in H^n. This confirms a conjecture of Gori, Sarfatti and Vlacci, who settled the two dimensional case.
Cite
@article{arxiv.2402.01378,
title = {On the geometry of zero sets of central quaternionic polynomials},
author = {Gil Alon and Elad Paran},
journal= {arXiv preprint arXiv:2402.01378},
year = {2024}
}