Hi, everyone:
I am reading a small expository paper on properties of CP^{2},
in which the intersection form is defined as an integral of
the wedge of two forms $w_1$, $w_2$, and these forms $w_1$, $w_2$ (no problem with
compact support, since CP^{2} is compact) seem to have been
obtained from the fundamental class [z] of H_{2}(CP^{2})--
a copy of CP^{1} (embedded in CP^{2}), after which we integrate $w:=w1\wedge w2$ to get the intersection number.

I am curious on whether I am reading the above correctly,
i.e., that the volume form in CP^{2} is obtained by using the fund.
class [z] in H_{2}. If not, would someone explain; if this is correct,
if we are we using some form of deRham's theorem to turn a purely
topological object like [z] into an object like $w$, for
which we must have a differentiable structure defined)?

Thanks in Advance.