Algebraic Geometry
《Algebraic Geometry》 · 第 12 页 · Chapter I，Exercise 2.8
A projective variety $Y\subseteq\mathbb P^n$ has dimension $n-1$ if and only if it is the zero set of a single irreducible homogeneous polynomial $f$ of positive degree. $Y$ is called a hypersurface in $\mathbb P^n$.