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Mathematics > Algebraic Geometry

arXiv:1809.08425 (math)
[Submitted on 22 Sep 2018 (v1), last revised 29 Dec 2021 (this version, v4)]

Title:Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

Authors:Yoshinori Hashimoto, Julien Keller
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Abstract:For a holomorphic vector bundle $E$ over a polarised Kähler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldson's functional is coercive on the set of Fubini-Study metrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein metrics implying slope stability.
Comments: 38 pages. Final version
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV); Differential Geometry (math.DG)
MSC classes: 14J60 (Primary) 14L24, 53C07 (Secondary)
Cite as: arXiv:1809.08425 [math.AG]
  (or arXiv:1809.08425v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1809.08425
Journal reference: Épijournal de Géométrie Algébrique, Volume 5 (January 3, 2022) epiga:6577
Related DOI: https://doi.org/10.46298/epiga.2022.6577

Submission history

From: Julien Keller [view email]
[v1] Sat, 22 Sep 2018 10:58:20 UTC (41 KB)
[v2] Tue, 12 Mar 2019 14:53:27 UTC (39 KB)
[v3] Wed, 17 Jun 2020 14:34:05 UTC (40 KB)
[v4] Wed, 29 Dec 2021 21:12:18 UTC (123 KB)
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