中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

多复变与复几何研讨班SCV&CG Seminar

Speaker: 青成昊博士 (Tsinghua University)

Inviter: 周向宇 院士

Language: Chinese

Title:  On the cohomology of pseudoeffective line bundles over holomorphically convex manifolds（I）

Time & Venue: 2025年12月2日（星期二） 10:00 - 11:00 & 南楼N913

Abstract:   In these talks, I will present my joint works with Prof. Xiankui Meng, Hongzhao Sun, and Prof. Xiangyu Zhou. We obtain a structure theorem for cohomology groups of pseudo-effective line bundles over holomorphically convex Kähler manifolds, which generalizes the results of Takegoshi, Demailly-Peternell-Schneider, Meng-Zhou. As applications, we first give an answer to a question proposed by Matsumura, and establish an injectivity theorem for purely log terminal pairs generalized to pseudo-effective line bundles with transcendental singularities. Then we show a Kawamata-Viehweg-Kollár-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact Kähler manifolds.

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Speaker: 青成昊博士 (Tsinghua University)

Inviter: 周向宇 院士

Language: Chinese

Title:  On the cohomology of pseudoeffective line bundles over holomorphically convex manifolds (II)

Time & Venue: 2025年12月2日（星期二） 11:00 - 12:00 & 南楼N913

Abstract:   In these talks, I will present my joint works with Prof. Xiankui Meng, Hongzhao Sun, and Prof. Xiangyu Zhou. We obtain a structure theorem for cohomology groups of pseudo-effective line bundles over holomorphically convex Kähler manifolds, which generalizes the results of Takegoshi, Demailly-Peternell-Schneider, Meng-Zhou. As applications, we first give an answer to a question proposed by Matsumura, and establish an injectivity theorem for purely log terminal pairs generalized to pseudo-effective line bundles with transcendental singularities. Then we show a Kawamata-Viehweg-Kollár-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact Kähler manifolds.