数学研究所

数学科学全国重点实验室

学术报告

代数几何研讨班

Speaker: 胡佳俊（清华大学）

Inviter: 欧文浩 副研究员

Language: Chinese

Title:Positivity in the shadow of Hodge index theorem

Time&Venue: 2025年6月5日（星期四）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.