2006/01/19 by Julien Keller, Keller, Julien
Mathematics · Physics and Astronomy · #14D21 #14L24 #32A25 #53C07 #53D20 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CV #math.DG #msc:14D21 #msc:14L24 #msc:32A25 #msc:53C07 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0601485
53 pages. To appear in Math. Annalen. Last section has been rewritten. Comments welcome !
openalex publication_date 2006/01/19 · arxiv created 2006/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle F over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on F coming from a construction of the Geometric Invariant Theory (G.I.T). These metrics are balanced in the sense of S.K. Donaldson. We prove that if there is a τ-Hermite-Einstein metric hHE on F, then there exists a sequence of such balanced metrics that converges and its limit is hHE. As a corollary, we obtain an approximation theorem for coupled Vortex equations that cover in particular the cases of Hermite-Einstein equations, Garcia-Prada and Bradlows's coupled Vortex equations and special Vafa-Witten equations.