Orbit Chern classes

Abstract

Let $G\subseteq \text{GL}(n,\mathbb{F})$ be a finite subgroup G of the general linear group over a field $\mathbb{F}$. Assume that $\mathbb{F}$ is algebraically closed. We show that the associated ring of polynomial invariants is characterized by its orbit Chern classes and vice versa. Moreover, the associated ring of polynomial invariants is characterized by its orbits on the dual space $V^{*}={({\mathbb{F}}^n)}^{*}$ and vice versa.

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13A50
• Secondary: 14L24

Keyword:

• Characteristic subalgebra
• invariant theory of finite groups
• orbit Chern classes

Additional information

Funding

This work is partially supported by a Simons Foundation Collaboration grant.