【学术报告】Fine structures on Hermitian symmetric spaces and minimal rational curves

报告人：黄国坚（深圳大学）

时 间：2025年12月4日14:30

地 点：海韵园实验楼S204

内容摘要:

Let $X$ be an irreducible Hermitian symmetric space of noncompact type. By Harish-Chandra realisation, $X\cong \Omega$ is realised as an irreducible bounded domain $\Omega\subset \mathbb{C}^n$. Let $M$ be the compact dual of $X$. Since $M$ is Fano and of Picard number one, there is a natural notion of minimal rational curves on $M$. We study the minimal rational curves intersecting $\Omega$.

Consider a point $b\in Reg(\partial \Omega)$. For the cone of minimal rational curves $\mathcal{V}_b$, Mok showed that the image $V_b:=\Omega\cap \mathcal{V}_b$ is holomorphically isometric to a complex unit ball.

In this talk, we briefly describe how such holomorphic isometry is obtained. Moreover, we construct from it a projection map $c_\Phi: \Omega\rightarrow \Phi$, where $\Phi\subset Reg(\partial\Omega)$ is a boundary component of $\partial \Omega$. Via the study of the moduli of all such projection maps, we recover a special case of the classical Fatou's Theorem on bounded symmetric domain, together with some fine structures related to the geometry of minimal rational curves. If time permit, we also mention some applications to rigidity problems in relation to Carath\'eodory geometry.

个人简介：

黄国坚，深圳大学助理教授。2017年在香港大学获得博士学位。2017年-2024年在韩国高等科学院和香港大学数学研究所做博士后。他的研究方向是多复变和复几何，主要研究复双曲性问题，函数超越性理论和霍奇理论等。在Math. Ann.,IMRN, Math. Z.等发表多篇论文。

联系人：孙锐然