$\DeclareMathOperator{\codim}{codim} \newcommand{\dprime}{^{\prime\prime}}\newcommand{\kk}{\mathbb{K}} \newcommand{\local}[2]{\mathcal{O}_{#2, #1}} \newcommand{\pp}{\mathbb{P}} \newcommand{\qq}{\mathbb{Q}} \newcommand{\rr}{\mathbb{R}} \DeclareMathOperator{\res}{Res} \newcommand{\scrL}{\mathcal{L}} \DeclareMathOperator{\sing}{Sing} \newcommand{\zz}{\mathbb{Z}}$The degree of a subvariety $X$ of a projective space $\pp^n$ defined over an algebraically closed field $\kk$ is the number of points of intersection of $X$ and a “generic” linear subspace of $\pp^n$ of “complementary dimension”, i.e. of dimension equal to $n – \dim(X)$.… Continue reading Degree of a projective variety