中科院数学与系统科学研究院
数学研究所
学术报告
复几何研讨班
报告人： 王隽永 博士（中科院数学院）
题 目：On the structure of projective varieties with semipositive curvature
时 间：2022.09.02（星期五），09:00-10:00
地 点：数学院南楼N219室
摘 要：Complex varieties with semipositive curvature have long been realized as having certain rigidity. From the differential-geometric viewpoint, this principle can be illustrated by the Bonnet-Myers theorem and the Cheeger-Colding theory. As for the algebro-geometric aspect, it is first revealed by Mori's and Siu-Yau's works on the Hartshorne-Frankel conjecture and people realized that the rigidity comes from the presence of rational curves. Inspired by the successive works to generalize this result (Mok-Zhong, Mok, Campana-Peternell, Demailly-Peternell-Schneider), and by the philosophy of the Minimal Model Program (MMP), mathematicians are interested in studying mildly singular projective varieties with nef anti-log canonical divisor. In this talk, I'll present the structure theorems of these varieties by revealing the structure of their rational curves. These are outcomes of my thesis work and of a series of joint works with Jie Liu, Shin-ichi Matsumura, Wenhao Ou, Xiaokui Yang and Guolei Zhong.
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