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- W1967654379 abstract "Letkbe an algebraically closed field and letS = k[x1,…,xm]. LetMbe a 2 × nmatrix of linear forms ofSand letI2(M) denote the ideal generated by the determinants of the 2 × 2 minors ofM. We study in this paper the minimal finite free resolution ofS/I2(M) as anS-module.Mcorresponds to a certain 2-dimensional vector spaceLofm × nmatrices, that is, to a matrix pencil. The Kronecker–Weierstrass theory of such matrix pencils provides a normal form forL, and we characterize the resolution ofS/I2(M) in terms of this normal form. In particular, if the general element ofLis injective, we explicitly construct the minimal resolution ofS/I2(M) by repeated application of the horseshoe lemma. For anyM, we express the regularity ofS/I2(M) as a function of the invariants ofL." @default.
- W1967654379 created "2016-06-24" @default.
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- W1967654379 date "1997-01-01" @default.
- W1967654379 modified "2023-10-17" @default.
- W1967654379 title "The Resolution of the Ideal of 2×2 Minors of a 2×nMatrix of Linear Forms" @default.
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- W1967654379 doi "https://doi.org/10.1006/jabr.1997.6801" @default.
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