Birational equivalence of exponential matrices

TL;DR

This paper classifies exponential matrices up to birational equivalence, providing a detailed categorization in characteristic zero for all sizes and specific classifications for sizes two and three in positive characteristic.

Contribution

It offers a comprehensive birational classification of exponential matrices, extending known results to positive characteristic cases for small sizes.

Findings

Classification into two types in characteristic zero

Birational classifications for 2x2 and 3x3 matrices in positive characteristic

Extension of birational equivalence theory to exponential matrices

Abstract

In this article, we consider birational equivalence of exponential matrices. In characteristic zero, we give a birational classification of exponential matrices of size $n$-by-$n$ $(n \geq 2)$, which consists of two types. And in positive characteristic, we give birational classifications of exponential matrices of sizes two-by-two and three-by-three, respectively.