# Continuity of the Yang-Mills flow on the set of semistable bundles

## TL;DR

This paper proves that the Yang-Mills flow on semistable bundles extends continuously to the compactification of the moduli space, linking geometric flow behavior with algebraic stability conditions.

## Contribution

It establishes the continuity of the Yang-Mills flow at infinity on semistable bundles, connecting the flow dynamics with the algebraic structure of the moduli space.

## Key findings

- Yang-Mills flow at infinity is continuous on semistable bundles
- The topology comparison aids in understanding the flow's limit behavior
- Provides a link between geometric analysis and algebraic geometry

## Abstract

A recent paper (arxiv.org:1810.00025) studied properties of a compactification of the moduli space of irreducible Hermitian-Yang-Mills connections on a hermitian bundle over a projective algebraic manifold. In this follow-up note, we show that the Yang-Mills flow at infinity on the space of semistable integrable connections defines a continuous map to the set of ideal connections used to define this compactification. Part of the proof involves a comparison between the topologies of the Grothendieck Quot scheme and the space of smooth connections.