Row Ideals and Fibers of Morphisms

TL;DR

This paper investigates the fibers of projective morphisms and explores algebraic properties related to ideals, including the analytic spread and linearity conditions, providing new characterizations and weaker properties preserved under powers.

Contribution

It introduces a novel characterization of the analytic spread via syzygy matrices and identifies a weaker linearity property maintained under ideal powers.

Findings

Characterization of analytic spread through syzygy matrix properties

Identification of a weaker linearity property preserved under powers

Insights into the behavior of linearly presented ideals and their powers

Abstract

We study the fibers of a projective morphism and some related algebraic problems. We characterize the analytic spread of a homogeneous ideal through properties of its syzygy matrix. Powers of linearly presented ideals need not be linearly presented, but we identify a weaker linearity property that is preserved under taking powers.