Mathematics – Commutative Algebra
Scientific paper
2005-12-18
Mathematics
Commutative Algebra
19 pages
Scientific paper
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 it is standard graded if and only if the graph is bipartite. We also give a general upper bound for the maximal degree of the generators of vertex cover algebras.
Herzog Juergen
Hibi Takayuki
Trung Ngo Viet
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