Existence of homogeneous ideals fitting into long Bourbaki sequences

Amasaki, Mutsumi

doi:10.1090/s0002-9939-99-04898-4

Proc. Amer. Math. Soc.

1999

DOI: 10.1090/s0002-9939-99-04898-4

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Existence of homogeneous ideals fitting into long Bourbaki sequences

Mutsumi Amasaki

Abstract: Abstract. For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

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Cited by 3 publications

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Liaison classes of modules

Nagel¹

2005

Journal of Algebra

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We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules. As a consequence, we show that the intermediate cohomology modules and properties like being perfect, Cohen-Macaulay, Buchsbaum, or surjective-Buchsbaum are preserved in even module liaison classes. Furthermore, we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one.

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Liaison classes of modules

Nagel¹

2005

Journal of Algebra

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Homogeneous prime ideals and graded modules fitting into long Bourbaki sequences

Amasaki

2001

Journal of Pure and Applied Algebra

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Constructing schemes with prescribed cohomology in arbitrary codimension

Migliore

Nagel

Peterson

2000

Journal of Pure and Applied Algebra

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Existence of homogeneous ideals fitting into long Bourbaki sequences

Abstract: Abstract. For any finitely generated torsion-free graded module over a polynomial ring, there exists a homogeneous ideal fitting into an exact sequence similar to a Bourbaki sequence even though its height is not restricted to two.

Cited by 3 publications

References 11 publications

Liaison classes of modules

Liaison classes of modules

Homogeneous prime ideals and graded modules fitting into long Bourbaki sequences

Constructing schemes with prescribed cohomology in arbitrary codimension

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