Gorenstein algebras, symmetric matrices, self-linked ideals, and symbolic powers
نویسندگان
چکیده
منابع مشابه
Gorenstein Algebras, Symmetric Matrices, Self-linked Ideals, and Symbolic Powers
Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...
متن کاملSymmetric Matrices , Self - Linked Ideals , and Symbolic Powers
Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...
متن کاملSymbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an algebra is normal and Cohen-Macaulay if the monomial ideal is squarefree. For a simple graph, the vertex cover algebra is generated by elements of degree 2, and ...
متن کاملSymbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated. Dedicated to Winfried Bruns on the occasion of his sixtieth birthday
متن کاملSymbolic Powers of Monomial Ideals and Vertex Cover Algebras
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated. Dedicated to Winfried Bruns on the occasion of his sixtieth birthday
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01960-0