# The variety defined by the matrix of diagonals is $F$-pure

## TL;DR

This paper proves that the algebraic variety defined by the determinant of the matrix of diagonals is $F$-pure across all matrix sizes and prime characteristics, and also identifies a system of parameters for it.

## Contribution

It establishes the $F$-purity of the variety defined by the determinant of the matrix of diagonals for all sizes and characteristics, and finds a system of parameters.

## Key findings

- The variety is $F$-pure in all positive prime characteristics.
- A system of parameters for the variety is explicitly constructed.
- The result applies universally to matrices of all sizes.

## Abstract

We prove that the variety defined by the determinant of the matrix of diagonals is $F$-pure for matrices of all sizes and in all positive prime characteristics. Moreover, we find a system of parameters for it.