## Regularization of closed positive currents and intersection theory.(English)Zbl 0777.32016

Let $$X$$ be a compact complex manifold and let $$T=i\partial\overline\partial\psi$$ be a closed positive current of bidegree (1,1) on $$X$$. Under some hypothesis on a lower bound for the Chern curvature of the tangent bundle $$TX$$, the current $$T$$ is proved to be the weak limit of closed currents $$T_ k={i\over\pi}\partial\overline\partial\psi_ k$$ with controlled negative parts; the functions $$\psi_ k$$ decrease to $$\psi$$ as $$k\to\infty$$ and can be chosen smooth on $$X$$. However the presence of positive Lelong numbers of $$T$$ results in some loss of positivity of $$T_ k$$.
This regularization is applied to relations between effective and numerically effective divisors, and to some problems of intersection theory.

### MSC:

 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) 32C30 Integration on analytic sets and spaces, currents 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)

### Keywords:

Lelong number; closed positive current; intersection theory