On the quotient of $\mathbb{C}^4$ by a finite primitive group of type (I)

TL;DR

This paper proves that the quotient of four-dimensional complex space by any finite primitive group of Type (I) is a rational variety, advancing understanding of rationality in algebraic geometry.

Contribution

It establishes the rationality of quotients of our-dimensional complex space by all finite primitive groups of Type (I), a significant step in the rationality problem.

Findings

The quotient our-dimensional space by such groups is rational.

The result applies to all finite primitive groups of Type (I).

This advances the classification of rational quotient varieties.

Abstract

We study rationality problem for the quotient of $\mathbb{C}^4$ by a finite primitive group $G$ of Type (I). We prove that this quotient is a rational variety for any such $G$.