We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-freeâ€¦ (More)

There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantalâ€¦ (More)

In this paper we describe the defining equations of the Rees a lg br and the special fiber ring of a truncationI of a complete intersection ideal in a polynomial ring over a fi eld with homogeneousâ€¦ (More)

We study the question of when the Ehrhart and toric rings of 0-1 polytopes are the same. In particular, we shall associate to each 0-1 polytope a labeled hypergraph, and examine the equality betweenâ€¦ (More)

Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneousâ€¦ (More)

We study the question of when 0-1 polytopes are normal or, equivalently, having the integer decomposition property. In particular, we shall associate to each 0-1 polytope a labeled hypergraph, andâ€¦ (More)

We provide the sufficient conditions for Rees algebras of modules to be Cohen-Macaulay, which has been proven in the case of Rees algebras of ideals in [11] and [4]. As it turns out theâ€¦ (More)