Related papers: On the Rees algebra of certain codimension two per…

Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals $I\subset R = K[x,y,z]$ we give the precise value of depth $R[It]$ and decide whether the…

In this paper we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring and the ideals are generated by subsets of a fixed weak regular sequence.

In this dissertation, we tackle the problem of describing the equations of the Rees algebra of I for I =(J,y), with J being of linear type. Throughout, such ideals are referred to as ideals of almost-linear type. In Theorem A, we give a…

Let $(A,\mathfrak{m})$ be an excellent normal local ring of dimension $d \geq 2$ with infinite residue field. Let $I$ be an $\mathfrak{m}$-primary ideal. Then the following assertions are equivalent: (i) The extended Rees algebra $A[It,…

The purpose of this paper is to prove that the symbolic Rees rings of ideals defining certain finite sets of points in the projective plane over an algebraically closed field are finitely generated using a ring theoretical criterion which…

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a "maximal" map f from M to…

In this paper we describe the equations defining the multi-Rees algebra $k[x_1,\dots,x_n][I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where the ideals are generated by subsets of $x_1,\dots,x_n$. We also show that a family of binomials whose leading…

Let (X,\sigma) be a symplectic space admitting a complex structure and let R(X,\sigma) be the corresponding resolvent algebra, i.e. the C*-algebra generated by the resolvents of selfadjoint operators satisfying canonical commutation…

We study the Rees algebra of a perfect Gorenstein ideal of codimension 3 in a hypersurface ring. We provide a minimal generating set of the defining ideal of these rings by introducing a modified Jacobian dual and applying a recursive…

This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative integers. The obtained results can be applied to…

We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.

An ideal $I \subset \mathbb{k}[x_1, \ldots, x_n]$ is said to have linear powers if $I^k$ has a linear minimal free resolution, for all $k$. In this paper we study the Betti numbers of $I^k$, for ideals $I$ with linear powers. The Betti…

The regularity of the Rees ring of the edge ideal of a finite simple graph is studied. We show that the matching number is a lower and matching number~$+1$ is an upper bound of the regularity, if the Rees algebra is normal. In general the…

In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.

This paper concerns a generalization of the Rees algebra of ideals due to Eisenbud, Huneke and Ulrich that works for any finitely generated module over a noetherian ring. Their definition is in terms of maps to free modules. We give an…

Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I. It is shown that the minimal generators of Rs(I) are in one to one correspondence with…

The aims of this work are to study Rees algebras of filtrations of monomial ideals associated to covering polyhedra of rational matrices with non-negative entries and non-zero columns using combinatorial optimization and integer…

The authors introduced the notion of $p_g$-ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In this note, we give several ring-theoretic characterization of…

Consider a height two ideal, $I$, which is minimally generated by $m$ homogeneous forms of degree $d$ in the polynomial ring $R=k[x,y]$. Suppose that one column in the homogeneous presenting matrix $\f$ of $I$ has entries of degree $n$ and…

Let I be a complete m-primary ideal of a regular local ring (R,m). In the case where R has dimension two, the beautiful theory developed by Zariski implies that I factors uniquely as a product of powers of simple complete ideals and each of…