Self-intersection of the diagonal of a curve
= Self-intersection of the diagonal of a curve
{title2=$\Delta_C^2=2-2g(C)$}
For a smooth projective <algebraic curve> $C$, the <normal bundle> of its diagonal in $C\times C$ is $TC$: on the diagonal the quotient of $TC\oplus TC$ by the diagonal subbundle is identified with $TC$ by taking the difference. The <self-intersection formula> therefore gives $\Delta_C^2=\deg TC=2-2g(C)$.