标题： 指数矩阵的有理等价性 显示英文标题

标题： Birational equivalence of exponential matrices

摘要： 设$k$为特征为$p \geq 0$的代数闭域，并设$\mathbb{G}_a$表示$k$的加法群。 我们给出指数矩阵与各种对象之间的一一对应关系，特别是给出大小为$n$-by-$n$的指数矩阵与$\mathbb{G}_a$-作用在$(n - 1)$-维射影空间之间的一一对应关系。 然后我们引入指数矩阵的有理等价，并开始对指数矩阵进行有理分类。 在特征零的情况下，我们给出大小为$n$-by-$n$ $(n \geq 2)$ 的指数矩阵的有理分类，该分类包括两种类型。 而在正特征情况下，我们给出了大小为二-by-二和三-by-三的指数矩阵的有理分类。 显示英文摘要

摘要： Let $k$ be an algebraically closed field of characteristic $p \geq 0$ and let $\mathbb{G}_a$ denote the additive group of $k$. We give one-to-one correspondences between exponentional matrices and various objects, and in particular give a one-to-one correspondence between exponential matrices of size $n$-by-$n$ and $\mathbb{G}_a$-actions on the $(n - 1)$-dimensional projective space. We then introduce birational equivalence of exponential matrices and start to classify exponential matrices birationally. 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.