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

epiga:6577 - Épijournal de Géométrie Algébrique, January 3, 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

Authors: 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
Published on: January 3, 2022
Accepted on: January 3, 2022
Submitted on: June 18, 2020
Keywords: Mathematics - Algebraic Geometry, Mathematics - Complex Variables, Mathematics - Differential Geometry, 14J60 (Primary) 14L24, 53C07 (Secondary)
Licence: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
Funding:
    Source : OpenAIRE Graph
  • Funder: French National Research Agency (ANR); Code: ANR-11-IDEX-0001
  • Extremal metrics and relative K-stability; Funder: French National Research Agency (ANR); Code: ANR-14-CE25-0010
  • Extremal metrics and relative K-stability; Funder: French National Research Agency (ANR); Code: ANR-11-LABX-0033

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