incompressible-fluid-equations
《incompressible-fluid-equations》 · 第 98 页 · Lecture 9「Determinantal Varieties」
We will start with what is called the generic determinantal variety. Let $M$ be the projective space associated to the vector space of $m\times n$ matrices. For each $k$, we let $M_k\subseteq M$ be the subset of matrices of rank $k$ or less; since this is just the common zero locus of the $(k+1)\times(k+1)$ minor determinants, which are homogeneous polynomials of degree $k+1$ on the projective space $M$, $M_k$ is a projective variety.