Work

Ranks of group-invariant sphere maps with source dimension greater than 2

Year: 2026

Type: article

Abstract: We study the target ranks for monomial sphere maps from Cn to CN that are invariant under some finite subgroup Γ of the unitary group on Cn. Previous work has established, for each such Γ, the existence of a threshold beyond which all target ranks are possible. The sharp threshold has been identified for most groups in source dimension 2 but not for higher source dimension n. In this paper, we obtain significant improvements in the estimate of this threshold for n>2 that illustrate that the situations for n = 2 and n>2 are qualitatively similar.

Source: Complex Variables and Elliptic Equations

DOI: 10.1080/17476933.2026.2717722

Authors: Jennifer Brooks, Samuel Liechty, Kyle Markham, Shogo Starr, Hailey Whetten

Institution: Brigham Young University

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203832782

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Cites: 10

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