Symbolic powers of monomial ideals and vertex cover algebras
نویسندگان
چکیده
منابع مشابه
Symbolic 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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We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...
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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...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2006.06.007