Equations of 2-linear ideals and arithmetical rank

TL;DR

This paper investigates ideals with 2-linear resolutions, focusing on their generators, arithmetical rank, and properties of associated fiber cones, providing new insights into their algebraic and geometric structure.

Contribution

It introduces new results on generators and arithmetical rank of 2-linear ideals, and characterizes fiber cones of certain lattice ideals as set-theoretic complete intersections.

Findings

Computed arithmetical rank for a class of projective curves with 2-linear resolution

Established that fiber cones of codimension two lattice ideals are set-theoretic complete intersections

Analyzed systems of generators for ideals with 2-linear resolutions

Abstract

In this paper we consider reduced homogeneous ideals $\Jcal\subset S$ of a polynomial ring $S$, having a 2-linear resolution. 1. We study systems of generators of $\Jcal\subset S$. 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 $\proj \Fcal(I_{\Lcal})$ of a lattice ideal $I_{\Lcal}$ of codimension two is a set theoretical complete intersection.