Vertex cover algebras of unimodular hypergraphs

2007/03/20 by Jürgen Herzog, Takayuki Hibi, Herzog, Jurgen +3
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.math/0703577

Abstract

It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic powers of monomial ideals.

Related

• Standard graded vertex cover algebras, cycles and leaves
• Symbolic powers of monomial ideals and vertex cover algebras
• Regularity of powers of cover ideals of unimodular hypergraphs
• Symbolic powers of monomial ideals which are generically complete intersections
• Toric rings arising from vertex cover ideals