电流的拟势和正则化及其应用
Quasi-potentials and regularization of currents, and applications
摘要：
设$Y$是紧致Kähler流形.我们证明了对角$Δ_Y$的Dinh和Sibony的弱正则化$K_n$（更多细节见第2节）在以下意义上与楔积相容：如果$T$是正$dd^c$ -闭$(p,p)$电流，$θ$是光滑的$(q,q)$形式，则存在正$dd^c$ -闭$(p+q,p+q)$电流$S_n$的序列，其质量收敛到0，使得对于所有$n$，$-S_n\leq K_n(T\wedge θ)-K_n(T)\wedge θ\leq S_n$。我们还证明了一个关于正闭合电流的准势的结果。我们给出了这些结果的两个应用。首先，我们证明了一个相应的兼容性与楔形产品的拉回算子在我们以前的文件中定义。其次，我们定义了正$dd^c$ -闭合电流的交积。这种交叉是对称的，并且具有局部性质。
英文摘要：
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 $-S_n\leq K_n(T\wedge θ)-K_n(T)\wedge θ\leq S_n$ 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.
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