arXiv subjects

Naoya Shimamoto

Publications and source records attributed to Naoya Shimamoto.

3 recordsLinked to original sources

arXiv2022

Configuration of five points in $\mathbb P^3$ and their limits

We give a classification of ordered five points in $\mathbb P^3$ under the diagonal action of $GL_4$ over an algebraically closed field of characteristic $0$, by an explicit description of the diagonal action of $GL_4$ on the quintuple of the projective varieties $\mathbb P^3$. This is the second simplest setting, where a reductive subgroup of $H$ of $G$ has an open orbit in a (generalised) flag variety $X$ of $G$ but $\#(H\backslash X)=\infty$. The closure relations among infinitely many orbits are also given.

math.RT↗

arXiv2022

Description of $GL_3$-orbits on the quadruple projective varieties

This article gives a description of the diagonal $GL_3$-orbits on the quadruple projective variety $(\mathbb P^2)^4$. We give explicit representatives of orbits, and describe the closure relations of orbits. A distinguished feature of our setting is that it is the simplest case where $\mathrm{diag}(GL_n)$ has infinitely many orbits but has an open orbit in the multiple projective space $(\mathbb P^{n-1})^m$.

math.RT↗

arXiv2019

Description of infinite orbits on multiple projective spaces

Let $G$ be the general linear group of the degree $n\geq 2$ over the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$. In this article, we give a description of orbit decomposition of the multiple projective space $G^m/P^m$ under the diagonal action of $G$ where $P$ is the maximal parabolic subgroup of $G$ such that $G/P\cong\mathbb{P}^{n-1}\mathbb{K}$. We also construct representatives of orbits. If $m\geq 4$, the number of orbits is infinite, and we give a description of those uncountably many orbits.

math.RT↗