Singular Nakano positivity of direct image sheaves

Speaker: Prof. Shin-ichi Matsumura，Tohoku University

Inviter: 周向宇

Title: Singular Nakano positivity of direct image sheaves

Language: English

Time & Venue: 2026.04.19  16:00-17:30  南楼N913

Abstract: Two notions of positivity, Nakano positivity and Griffiths positivity, exist for the Chern curvature of vector bundles. The theory of Griffiths positivity for singular metrics is already well-developed, and via its connection to the -extension theorem with optimal estimates by Guan-Zhou, the positivity of direct image sheaves of relative canonical bundles, which is particularly important for applications in algebraic geometry, has been established. In contrast, the theory of Nakano positivity for singular metrics is still under development. In this talk, I will introduce several aspects of Nakano positivity for singular metrics and explain my recent work on singular Nakano positivity for direct image sheaves. This work is based on joint work with Inayama (Tokyo University of Science) and Watanabe (Chuo University).