2016/12/30 by Nicholas Buchdahl, Andrei Teleman, Matei Toma
Mathematics · #Algebraic Geometry and Number Theory #Base (topology) #Combinatorics #Compactification (mathematics) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Instanton #Locus (genetics) #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Pure mathematics #Topology (electrical circuits) #Torsion (gastropod) #math.CV #math.DG #msc:32G13 #msc:53C07 #msc:53C55
paper · pdf · doi:10.1112/topo.12029
arxiv created 2016/12/30 · openalex publication_date 2017/10/19 · arxiv updated 2017/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that any flat family ( F u ) u ∈ U of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus U ss : = u ∈ U | F u is slope semi-stable with values in the Donaldson–Uhlenbeck compactification of the corresponding instanton moduli space. In the general (possibly non-Kählerian) case, the Donaldson–Uhlenbeck compactification is not a complex space, and the set U ss can be a complicated subset of the base space U that is neither open or closed in the classical topology, nor locally closed in the Zariski topology. This result provides an efficient tool for the explicit description of Donaldson–Uhlenbeck compactifications on arbitrary Gauduchon surfaces.