Continuity of the Yang-Mills flow on the set of semistable bundles
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.02312
- arXiv:
- arXiv:1904.02312
- Bibcode:
- 2019arXiv190402312S
- Keywords:
-
- Mathematics - Differential Geometry
- E-Print:
- 15 pages