| Résume | Around the year 1979, inspired by the Aleksandrov-Fenchel inequalities in convex geometry, Khovanskii and Teissier discovered independently deep inequalities in algebraic geometry which now are called Khovanskii-Teissier inequalities. These inequalities present a nice relationship between convex geometry and algebraic geometry. A natural problem is how to characterize the equality case in these inequalities for a pair of big and nef classes, which was first considered by B. Teissier around the year 1980. Based on the differentiability of the volume function for divisor classes, this problem has been solved for divisor classes on algebraic varieties by Boucksom-Farve-Jonsson. Through a different strategy, using Monge-Ampère equations in big cohomology classes and somebasic pluripotential theory, we solved Teissier's proportionality problem for transcendental classes over compact Kähler manifolds. Indeed, the equality characterization for a pair of classes could be extended easily to any number of big and nef classes. This talk is mainly based on the joint work with Jixiang Fu. |
