Self-intersection of an algebraic curve
= Self-intersection of an algebraic curve
{title2=$C^2=\deg\mathcal O_C(C)$}
= Algebraic self-intersection
{synonym}
For a proper integral Cartier curve $C$ on a smooth algebraic surface, its self-intersection is $\deg\mathcal O_C(C)$. If $C$ is smooth, this is the degree of its normal line bundle. It is defined over any algebraically closed field, without requiring an associated real or complex manifold.
// Target: geometry-and-topology.bigb