%0 Journal Article
%T Instanton moduli spaces on non-Kählerian surfaces. Holomorphic models around the reduction loci
%+ Institut de Mathématiques de Marseille (I2M)
%A Teleman, Andrei
%< avec comité de lecture
%@ 0393-0440
%J Journal of Geometry and Physics
%I Elsevier
%V 91
%P 66–87
%8 2015-05
%D 2015
%Z 1411.4985
%R 10.1016/j.geomphys.2015.01.007
%K Instanton moduli space
%K Stable holomorphic bundles
%K Class VII surfaces
%K Flips
%Z MSC 53C55, 53C07, 32G13
%Z Mathematics [math]/Differential Geometry [math.DG]
%Z Mathematics [math]/Complex Variables [math.CV]
%Z Mathematics [math]/Algebraic Geometry [math.AG]Journal articles
%X Let $\mathcal{M}$ be a moduli space of polystable rank 2-bundles bundles with fixed determinant (a moduli space of $\mathrm{PU}(2)$-instantons) on a Gauduchon surface with $p_g=0$ and $b_1=1$. We study the holomorphic structure of $\mathcal{M}$ around a circle $\mathcal{T}$ of regular reductions. Our model space is a "blowup flip passage", which is a manifold with boundary whose boundary is a projective fibration, and whose interior comes with a natural complex structure. We prove that a neighborhood of the boundary of the blowup $\hat{\mathcal{M}}_{\mathcal{T}}$ of $\mathcal{M}$ at $\mathcal{T}$ can be smoothly identified with a neighborhood of the boundary of a "flip passage" $\hat Q$, the identification being holomorphic on $\mathrm{int}(\hat Q)$.
%G English
%L hal-01221942
%U https://hal.science/hal-01221942
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ ANR