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On multigraded resolutions

  • Winfried Bruns (a1) and Jürgen Herzog (a2)
Abstract

This paper was initiated by a question of Eisenbud who asked whether the entries of the matrices in a minimal free resolution of a monomial ideal (which, after a suitable choice of bases, are monomials) divide the least common multiple of the generators of the ideal. We will see that this is indeed the case, and prove it by lifting the multigraded resolution of an ideal, or more generally of a multigraded module, keeping track of how the shifts ‘deform’' in such a lifting; see Theorem 2·1 and Corollary 2·2.

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[2]L. L. Avramov and E. Golod . On the homology of the Koszul complex of a local Gorenstein ring. Math. Notes 9 (1971), 3032.

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[5]D. A. Buchsbaum and D. Eisenbud . Algebra structures for finite free resolutions, and some structure theorems for ideals in codimension 3. Amer. J. Math. 99 (1977), 447485.

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[13]P. Mani . Spheres with a few vertices. J. Combinat. Theory Ser. A 13 (1972), 346352.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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