A simple limit for slope instability

TL;DR

This paper links slope instability of varieties to a simpler slope instability condition for certain bundles, simplifying the analysis of stability in algebraic geometry.

Contribution

It identifies a special case where slope instability of varieties reduces to a more manageable bundle stability problem, facilitating easier computations.

Findings

Slope instability of varieties can correspond to bundle slope instability in specific cases.

The approach simplifies stability analysis for varieties of general type.

Provides a new perspective connecting variety and bundle stability conditions.

Abstract

Ross and Thomas have shown that subschemes can K-destabilise polarised varieties, yielding a notion known as slope (in)stability for varieties. Here we describe a special situation in which slope instability for varieties (for example of general type) corresponds to a slope instability type condition for certain bundles, making the computations almost trivial.