= Projective lines generate a unimodular intersection form
{title2=$h\cdot h=1$}
The <fundamental class> of a <complex projective line> generates $H_2(\mathbb{CP}^2;\mathbb Z)$. Two distinct projective lines are homologous and meet at one transverse point. In complex affine coordinates their two complex tangent lines concatenate to the complex <orientation> of the plane, so the signed intersection is $+1$. The integral <intersection form> therefore has matrix $(1)$, giving a <unimodular intersection pairing>. This computes a self-intersection through distinct representatives of the same class.
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