Let $X$ be a complex manifold. Any dimension $p$ subvariety(or reduced analytic subscheme) will determine a real closed positive $(p,p)$-current. But the converse is not true.

My question:

1. Is there a typical example of a closed positive real $(p,p)$-form which is not a subvariety?

2. Intuitively, what is the essential difference between closed positive real $(p,p)$-form and subvariety?

Let $X$ be a complex manifold. Any dimension $p$ subvariety(or reduced analytic subscheme) will determine a real closed positive $(p,p)$-current. But the converse is not true.

My question:

1. Is there a typical example of a closed positive real $(p,p)$-form which is not a subvariety?

2. Intuitively, what is the essential difference between closed positive real $(p,p)$-form and subvariety?

I realize there are some trivial examples. For example, let $A\subseteq X$ be a subvariety and $[A]$ be the current associated to it. Then $\lambda[A]$ is not a current from subvariety. But is there any essential examples?