An ideal I in a polynomial ring S has linear powers if all the powers I k of I have a linear free resolution.We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers. The required genericity is expressed in terms of the heights of the ideals of lower order minors. In particular we prove that every rational normal scroll has linear powers.
Maximal minors and linear powers
CONCA, ALDO;VARBARO, MATTEO
2015-01-01
Abstract
An ideal I in a polynomial ring S has linear powers if all the powers I k of I have a linear free resolution.We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers. The required genericity is expressed in terms of the heights of the ideals of lower order minors. In particular we prove that every rational normal scroll has linear powers.
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(2015) Bruns Conca Varbaro - Maximal minors and linear powers.pdf
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