Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

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

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a3


Benjamin Sibley (Université Libre de Bruxelles, Belgium)

Richard Wentworth (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)


A recent paper [16] 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.

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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