Projective hypersurface
= Projective hypersurface
{title2=$X_d$}
A degree-$d$ projective hypersurface $X_d\subseteq\mathbb P_k^n$ is the <closed subscheme> cut out by one nonzero homogeneous polynomial of degree $d$.
This is a homogeneous-polynomial <hypersurface> in projective space.