中科院数学与系统科学研究院
数学研究所
学术报告
代数几何研讨班
题 目：Algebraic reverse Khovanskii-Teissier inequality and Okounkov bodies
时 间：2021.12.17（星期五）下午
地 点：腾讯会议：344 711 856
简 介：The lectures are devoted to proving the reverse Khovanskii-Teissier inequality in the algebraic setting. Let $X$ be a projective variety of dimension $n$ over an algebraically closed field of arbitrary characteristic and let $A, B, C$ be nef divisors on $X$. We will show that for any integer $1\leq k\leq n-1$, $$(B^k\cdot A^{n-k})\cdot (A^k\cdot C^{n-k})\geq \frac{k!(n-k)!}{n!}(A^n)\cdot (B^k\cdot C^{n-k}).$$ The same inequality in the analytic setting was obtained by Lehmann and Xiao for compact K\"ahler manifolds using the Calabi--Yau theorem.
n 时 间：14:30-16:00
报告人：李志远 研究员（复旦大学）
摘 要：We will give an overview of the (multipoint) Okounkov bodies and their relation to the volumes of big divisors. This is mainly due to the work of Lazarsfeld-Mustata and Trusiani.
n 时 间：16:10-17:40
报告人：江辰 研究员（复旦大学）
摘 要：We will explain how to apply the (multipoint) Okounkov bodies to prove the inequality. We also discuss applications of this inequality to B\'ezout-type inequalities and inequalities on degrees of dominant rational self-maps.
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