Degree of an algebraic variety
= Degree of an algebraic variety
{title2=$\deg X$}
{wiki}
The degree of a projective <algebraic variety> of dimension $r$ is the length, with <intersection multiplicities>, of its intersection with a sufficiently general linear subspace of complementary codimension. Equivalently, its <Hilbert polynomial> has leading coefficient $\deg X/r!$. For a <projective curve>, a general hyperplane section measures this degree.