Hermitian-Einstein connections and stable vector bundles over compact complex surfaces

DOI10.1007/BF01450081zbMath0617.32044MaRDI QIDQ1821920

Nicholas P. Buchdahl

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164389

zbMATH Keywords

stable holomorphic vector bundlecompact complex surfaceHermitian-Einstein connection

Mathematics Subject Classification ID

Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Compact complex surfaces (32J15) Connections (general theory) (53C05)

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Polystable bundles and representations of their automorphisms ⋮ Holomorphic bundles and the moduli space of \(N=1\) supersymmetric heterotic compactifications ⋮ Algebraic methods for vector bundles on non-Kähler elliptic fibrations ⋮ Higgs bundles over foliation manifolds ⋮ Moduli spaces of simple bundles and Hermitian-Einstein connections ⋮ Generalized Donaldson functionals and related nonlinear partial differential equations ⋮ The heterotic superpotential and moduli ⋮ On the blow-up set of the Yang-Mills flow on Kähler surfaces ⋮ Hermitian-Einstein metrics for Higgs bundles over complete Hermitian manifolds ⋮ Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ²ⁿ⁺¹ ⋮ Instantons, Poisson structures and generalized Kähler geometry ⋮ Heterotic backgrounds via generalised geometry: moment maps and moduli ⋮ Yang-Mills fields on cylindrical manifolds and holomorphic bundles. I ⋮ Yang-Mills fields on cylindrical manifolds and holomorphic bundles. II ⋮ Semi-stable holomorphic vector bundles over generalized Kähler manifolds ⋮ Semi-stability for bi-holomorphic pairs over compact bi-Hermitian Gauduchon manifolds ⋮ A Liouville theorem on complete non-Kähler manifolds ⋮ Canonical metrics on holomorphic Courant algebroids ⋮ The non-abelian Hodge correspondence on some non-Kähler manifolds ⋮ Canonical metrics on holomorphic filtrations over compact Hermitian manifolds ⋮ A Kobayashi-Hitchin correspondence for \(I_{\pm}\)-holomorphic bundles ⋮ Instantons and curves on class VII surfaces ⋮ Stable Higgs bundles on compact Gauduchon manifolds ⋮ The ADHM-like constructions for instantons on \(\mathbb{CP}^2\) and three-dimensional gauge theories ⋮ Non-Kähler Calabi-Yau geometry and pluriclosed flow ⋮ Coupled Kähler-Einstein and Hermitian-Yang-Mills equations ⋮ Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures ⋮ The gradient flow of Higgs pairs ⋮ Donaldson theory in non-Kählerian geometry ⋮ Flat bundles on \(G/\Gamma\) and stability ⋮ Monopoles on Sasakian three-folds ⋮ The Hitchin-Kobayashi correspondence for holomorphic pairs over non-Kähler manifolds ⋮ Semistable Higgs bundles over compact Gauduchon manifolds ⋮ Semistable twisted holomorphic chains on non-compact Kähler manifolds ⋮ Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. I: Generalities and the one-dimensional case ⋮ Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds ⋮ Stable bundles on hypercomplex surfaces ⋮ Existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles ⋮ Stable bundles on non-Kähler elliptic surfaces ⋮ The Nekrasov conjecture for toric surfaces ⋮ The pseudo-effective cone of a non-Kählerian surface and applications ⋮ Canonical metrics on holomorphic bundles over compact bi-Hermitian manifolds ⋮ Kobayashi-Hitchin correspondence for twisted vector bundles ⋮ Analytically stable Higgs bundles on some non-Kähler manifolds ⋮ Generalized Kähler geometry of instanton moduli spaces ⋮ The Anomaly flow on unimodular Lie groups ⋮ The classification of monopoles for the classical groups ⋮ Semi-stability for holomorphic pairs on compact Gauduchon manifolds ⋮ Dirichlet problem for Hermitian Yang-Mills-Higgs equations over Hermitian manifolds ⋮ Stability and holomorphic connections on vector bundles over LVMB manifolds ⋮ Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces. ⋮ Sequences of stable bundles over compact complex surfaces ⋮ Donaldson theory on non-Kählerian surfaces and class VII surfaces with \(b_2=1\) ⋮ Higgs bundles over non-compact Gauduchon manifolds ⋮ Instanton moduli spaces on non-Kählerian surfaces. Holomorphic models around the reduction loci

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