Quasi-potentials and regularization of currents, and applications

2011/11/01 by Truong, Tuyen Trung
#32H50 #37F99 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.0278

Abstract

Let Y be a compact Kähler manifold. We show that the weak regularization K_n of Dinh and Sibony for the diagonal Δ_Y (see Section 2 for more detail) is compatible with wedge product in the following sense: If T is a positive dd^c-closed (p,p) current and θ is a smooth (q,q) form then there is a sequence of positive dd^c-closed (p+q,p+q) currents S_n whose masses converge to 0 so that -S_n≤ K_n(T\wedge θ)-K_n(T)\wedge θ≤ S_n for all n. We also prove a result concerning the quasi-potentials of positive closed currents. We give two applications of these results. First, we prove a corresponding compatibility with wedge product for the pullback operator defined in our previous paper. Second, we define an intersection product for positive dd^c-closed currents. This intersection is symmetric and has a local nature.

Related

• Regularization of currents and entropy
• Intersection of positive closed currents of higher bidegree
• Intersection of Positive Closed Currents
• Pull-back of currents by meromorphic maps
• Super-potentials, densities of currents and number of periodic points\n for holomorphic maps