Symbolic powers of monomial ideals and vertex cover algebras

2005/12/18 by Juergen Herzog, Takayuki Hibi, Herzog, Juergen +3 · 3 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Algebraic structures and combinatorial models #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0512423

Abstract

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.

Cited by

• Graded families of ideals and convex regions
• Rational symbolic powers of ideals
• Admissible set and squarefree-power-like function with applications to squarefree symbolic powers

Related

• Standard graded vertex cover algebras, cycles and leaves
• Vertex cover algebras of unimodular hypergraphs
• Symbolic powers of monomial ideals which are generically complete intersections
• Splittings and symbolic powers of square-free monomial Ideals
• Symbolic powers of vertex cover ideals