Speaker: 胡佳俊，清华大学

Inviter: 欧文浩副研究员

Title: Positivity in the shadow of Hodge index theorem

Language: Chinese

Time & Venue: 2025.06.05 14:00-15:00 思源楼S813

Abstract: We investigate the power of the Hodge index theorem from several perspectives. (1) For Lefschetz-type operators arising from complete intersections of nef classes, we provide a complete characterization of the kernel face relative to the pseudo-effective cone. (2) We propose a new approach to Teissier’s proportionality problem, grounded in the validity of the hard Lefschetz property. Our results extend those of Boucksom–Favre–Jonsson and Fu–Xiao to broader contexts, including certain algebraic cycle classes defined by reducible subvarieties. (3) Furthermore, we strengthen the proportionality characterization by comparing various quantitative deficits and establishing stability estimates. We also discuss two sharper quantitative stability estimates, closely related to complex Monge-Ampère equations and Newton-Okounkov bodies. Based on a joint work with Jian Xiao.