Syzygies of Codimension 2 Lattice Ideals

Syzygies, Ideals of Height Two, and Vector Bundles

This paper deals with recent progress and connections between several open problems in the theory of syzygies, ideals of height two, factorial rings of small embedding codimension, and vector bundles of small rank. Throughout the paper (unless stated otherwise) R will denote a regular local ring with maximal ideal m. All modules will be finitely generated. The central problem which we will disc...

A Note on the Multiplicity of Determinantal Ideals

Abstract. Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous k-algebra, the multiplicity is bounded above by a function of the maximal degrees of the syzygies and below by a function of the minimal degrees of the syzygies. The goal of this paper is to establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay alg...

Lifting Problem in Codimension 2 and Initial Ideals

APPROXIMATE IDENTITY IN CLOSED CODIMENSION ONE IDEALS OF SEMIGROUP ALGEBRAS

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

Equations of 2-linear Ideals and Arithmetical Rank

1 In this paper we consider reduced homogeneous ideals J ⊂ S of a polynomial ring S, having a 2-linear resolution. 1. We study systems of generators of J ⊂ S. 2. We compute the arithmetical rank for a large class of projective curves having a 2-linear resolution. 3. We show that the fiber cone projF(IL) of a lattice ideal IL of codimension two is a set theoretical complete intersection.