Heights of Ideals of Minors

Details Heights of Ideals of Minors Heights of Ideals of Minors

2002-09-15

arxiv.org/abs/math/0209184v1

Mathematics

Commutative Algebra

21 pages, in AMS TeX

Scientific paper

The classical "generalized principal ideal theorems" of Macaulay, Eagon-Northcott, and others give sharp bounds on the heights of determinantal ideals in arbitrary rings. But in regular local rings (or graded polynomial rings) these are far from sharp, and various questions about vector bundles, as well as other questions in commutative algebra, amount to asking what the real bounds are. We give partial answers, and more generally we prove new height bounds in local rings of given embedding codimension. Our theorems extend and sharpen results of Faltings and Bruns.

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