Yoshinori Hashimoto ; Julien Keller - Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles

epiga:6577 - Épijournal de Géométrie Algébrique, 3 janvier 2022, Volume 5 - https://doi.org/10.46298/epiga.2022.6577
Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundlesArticle

Auteurs : Yoshinori Hashimoto ; Julien Keller

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.

Comment: 38 pages. Final version

https://doi.org/10.46298/epiga.2022.6577
Source : arXiv.org:1809.08425
Volume : Volume 5
Publié le : 3 janvier 2022
Accepté le : 3 janvier 2022
Soumis le : 18 juin 2020
Mots-clés : Mathematics - Algebraic Geometry, Mathematics - Complex Variables, Mathematics - Differential Geometry, 14J60 (Primary) 14L24, 53C07 (Secondary)
Licence : Attribution - Partage dans les Mêmes Conditions 4.0 International (CC BY-SA 4.0)
Financement :
    Source : OpenAIRE Graph
  • Extremal metrics and relative K-stability; Financeur: French National Research Agency (ANR); Code: ANR-14-CE25-0010
  • Extremal metrics and relative K-stability; Financeur: French National Research Agency (ANR); Code: ANR-11-LABX-0033
  • Extremal metrics and relative K-stability; Financeur: French National Research Agency (ANR); Code: ANR-11-IDEX-0001

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