Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects
- 2 Three Lectures on Quadratic Enumerative Geometry
- 3 Flat Torsors in Complex Geometry
- 4 Universal Chern Classes on the Moduli of Bundles
- 5 Linear Stability of Coherent Systems and Applications to Butler’s Conjecture
- 6 A Kobayashi–Hitchin Correspondence for General Coherent Systems
- 7 On the Injectivity and Non-injectivity of the l-Adic Cycle Class Maps
- 8 A Primer on Zeta Functions and Decomposition Spaces
- 9 Atiyah–Bott Localization in Equivariant Witt Cohomology
- 10 Base Loci, Semiampleness, and Parallelizable Manifolds
- 11 Recent Developments on Compactifications of Stacks of Shtukas
- 12 A Common Generalisation of the André–Oort and André–Pink–Zannier Conjectures
- References
6 - A Kobayashi–Hitchin Correspondence for General Coherent Systems
Published online by Cambridge University Press: 31 October 2025
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects
- 2 Three Lectures on Quadratic Enumerative Geometry
- 3 Flat Torsors in Complex Geometry
- 4 Universal Chern Classes on the Moduli of Bundles
- 5 Linear Stability of Coherent Systems and Applications to Butler’s Conjecture
- 6 A Kobayashi–Hitchin Correspondence for General Coherent Systems
- 7 On the Injectivity and Non-injectivity of the l-Adic Cycle Class Maps
- 8 A Primer on Zeta Functions and Decomposition Spaces
- 9 Atiyah–Bott Localization in Equivariant Witt Cohomology
- 10 Base Loci, Semiampleness, and Parallelizable Manifolds
- 11 Recent Developments on Compactifications of Stacks of Shtukas
- 12 A Common Generalisation of the André–Oort and André–Pink–Zannier Conjectures
- References
Summary
General coherent systems are defined as pairs (ℰ,S), where ℰ
is a rank-n holomorphic vector bundle and S is a vector subspace of H0(ℰρ)
, ℰρ
is the vector bundle induced by ℰ
and a representation ρ:GL(n)→GL(W)
. In this work we will prove a Kobayashi-Hitchin correspondence for a simple general coherent system. This is done using well known gauge theoretic techniques which were developed by Bradlow, Garcia-Prada and Mundet i Riera. The focus of this paper is proving that the stability condition that arises is equivalent to the one defined by Alexander Schmitt.
Information
- Type
- Chapter
- Information
- Moduli, Motives and BundlesNew Trends in Algebraic Geometry, pp. 183 - 200Publisher: Cambridge University PressPrint publication year: 2025
References
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