Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Special Issue in Honor of Duong H. Phong
Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove
Continuity of the Yang–Mills flow on the set of semistable bundles
Pages: 909 – 931
A recent paper  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.
Yang–Mills flow, semistable bundles, Donaldson–Uhlenbeck compactification
2010 Mathematics Subject Classification
Primary 32G13, 53C07. Secondary 14J60.
R.W.’s research supported in part by NSF grant DMS-1906403. The authors also acknowledge support from NSF grants DMS-1107452, -1107263, -1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network).
Received 17 March 2019
Accepted 15 November 2019
Published 14 June 2021