Exceptional Algebraic sets for discrete groups of $PSL(3,\Bbb{C})$

TL;DR

This paper characterizes the structure of exceptional algebraic sets for infinite discrete groups in PSL(3,C), showing they are composed of specific algebraic curves such as lines, Veronese curves, or cubic curves.

Contribution

It provides a classification of the possible exceptional algebraic sets for such groups, identifying their geometric composition.

Findings

Exceptional algebraic sets are finite unions of lines, Veronese curves, or cubic curves.

The classification narrows down the geometric structures of these sets.

The result advances understanding of the algebraic and geometric properties of discrete groups in PSL(3,C).

Abstract

In this note, we show that the exceptional algebraic set of an infinite discrete group in $PSL(3,\Bbb{C})$ should be a finite union of complex lines, copies of the Veronese curve or copies of the cubic $xy^2-z^3$.