Ideals Generated by Principal Minors

摘要: A minor is principal means it defined by the same row and column indices. Let $X$ be a square generic matrix, $K[X]$ polynomial ring in entries of $X$, over an algebraically closed field, $K$. For fixed $t\leq n$, let $\mathfrak P_t$ denote ideal generated size $t$ minors $X$. When $t=2$ resulting quotient $K[X]/\mathfrak P_2$ normal complete intersection domain. $t>2$ we break problem into cases depending on rank, $r$, We show when $r=n$ for any $t$, respective images P_{n-t}$ localized ring, where invert $\det X$, are isomorphic. From that algebraic set given P_{n-1}$ has codimension $n$ component, plus 4 component determinantal (which all submaximal $X$). $n=4$ two components linked, prove some consequences.