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• W2963987457 abstract "A minor is principal means it is defined by the same row and column indices. We study ideals generated by principal minors of size $tleq n$ of a generic $ntimes n$ matrix $X$, in the polynomial ring generated over an algebraically closed field by the entries of $X$. When $t=2$ the resulting quotient ring is a normal complete intersection domain. We show for any $t$, upon inverting $det X$ the ideals given respectively by the size $t$ and the size $n-t$ principal minors become isomorphic. From that we show the algebraic set given by the size $n-1$ principal minors has a codimension $4$ component defined by the determinantal ideal, plus a codimension $n$ component. When $n=4$ the two components are linked, and in fact, geometrically linked." @default.
• W2963987457 created "2019-07-30" @default.
• W2963987457 creator A5049912301 @default.
• W2963987457 date "2015-01-01" @default.
• W2963987457 modified "2023-09-24" @default.
• W2963987457 title "Ideals generated by principal minors" @default.
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• W2963987457 doi "https://doi.org/10.1215/ijm/1475266403" @default.
• W2963987457 hasPublicationYear "2015" @default.
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