Immanant varieties

TL;DR

This paper introduces immanant varieties linked to finite group characters, unifying several classical varieties and exploring their algebraic and combinatorial properties, including generators for Chow vector spaces.

Contribution

It defines immanant varieties associated with simple characters, connecting them to known varieties and developing combinatorial tools for their Chow spaces.

Findings

Immanant varieties include Segre, Grassmannians, and Chow varieties.

Generators for Chow vector spaces of certain immanant varieties are provided.

The paper explores combinatorial structures via incidence stratifications.

Abstract

We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional character $\chi$, we define $\chi$-matroids by a maximality property. For trivial characters, by exploring the combinatorics of incidence stratifications, we provide a set of generators for the Chow vector spaces of the corresponding immanant varieties.