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The Resolution of the Ideal of 2 × 2 Minors of a 2 × nMatrix of Linear Forms

✍ Scribed by Michael L. Catalano-Johnson

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
136 KB
Volume
187
Category
Article
ISSN
0021-8693

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✦ Synopsis

2=n matrix of linear forms of S and let I M denote the ideal generated by the 2 determinants of the 2 = 2 minors of M. We study in this paper the minimal finite Ž . free resolution of SrI M as an S-module. M corresponds to a certain 2-2 dimensional vector space L of m = n matrices, that is, to a matrix pencil. The Kronecker᎐Weierstrass theory of such matrix pencils provides a normal form for Ž . L, and we characterize the resolution of SrI M in terms of this normal form. In 2 particular, if the general element of L is injective, we explicitly construct the Ž . minimal resolution of SrI M by repeated application of the horseshoe lemma.

2

Ž .

For any M, we express the regularity of SrI M as a function of the invariants of 2 L.

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