Intersection of positive closed currents

초록

In this lecture, we will discuss the wedge product of positive closed currents. Positive closed currents are measure-theoretic method to study geometric objects. For technical reasons, the theory is well developed for positive closed $(1,1)$-currents. First, we will review some basic materials concerning positive closed currents and the wedge product of positive closed $(1,1)$-currents. Next, we study the theory of superpotentials on the projective spaces for the higher bidegree. Also, why it is not easy to extend superpotentials to all positive closed currents on a general compact Kaehler manfold will be treated. If time allows, we will talk about the theory of density introduced by Dinh-Sibony.