14 citations · 34 across the 7 of their papers we have counts for
7 papers
An Analytic Application of Geometric Invariant Theory II: Coarse Moduli Spaces
Nicholas Buchdahl, Georg Schumacher
In [arXiv:2008.04625] the authors constructed a classifying space for polystable holomorphic vector bundles on a compact Kähler manifold using analytic GIT theory. The aim of this…
An Analytic Application of Geometric Invariant Theory
Nicholas Buchdahl, Georg Schumacher
Given a compact Kähler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic…
Polystability and the Hitchin-Kobayashi correspondence
Nicholas Buchdahl, Georg Schumacher
Using a quasi-linear version of Hodge theory, holomorphic vector bundles in a neighbourhood of a given polystable bundle on a compact Kaehler manifold are shown to be (poly)stable…
On the Donaldson-Uhlenbeck compactification of instanton moduli spaces on class VII surfaces
Nicholas Buchdahl, Andrei Teleman, Matei Toma
We study the following question: Let be a compact Gauduchon surface, be a differentiable rank vector bundle on , be a fixed holomorphic struc…
A continuity theorem for families of sheaves on complex surfaces
Nicholas Buchdahl, Andrei Teleman, Matei Toma
We prove that any flat family of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus $U^{\mathrm {ss}}:…
Blowups and gauge fields
Nicholas P. Buchdahl
The relationship between stable holomorphic vector bundles on a compact complex surface and the same such objects on a blowup of the surface is investigated, where "stability" is w…
Sequences of stable bundles over a compact complex surface
Nicholas P. Buchdahl
When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact comp…