Criteria for componentwise linearity

TL;DR

This paper provides characteristic-free criteria to determine when graded ideals are componentwise linear, and applies these criteria to classify such ideals within Gorenstein, determinantal, and submaximal minors ideals.

Contribution

It introduces new characteristic-free conditions for componentwise linearity and classifies these ideals in specific algebraic classes.

Findings

Established characteristic-free criteria for componentwise linearity.

Classified componentwise linear ideals among Gorenstein, determinantal, and symmetric minors.

Provided a comprehensive framework for understanding componentwise linearity in various ideal classes.

Abstract

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix.