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Instantons and framed sheaves on Kähler Deligne–Mumford stacks
Philippe Eyssidieux1; Francesco Sala2
1 Institut Fourier, Université Grenoble-Alpes, Grenoble, France
2 Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 3, pp. 599-628.

We provide stacky generalizations of classical gauge-theoretic results inspired by Donaldson, the Uhlenbeck–Yau theorem and variants due to Bando and his collaborators. Moreover, we show an application of this machinery in the study of ALE spaces.

Nous donnons une généralisation champêtre de résultats classiques de théorie de jauge, comme la caractérisation par Donaldson des instantons sur ℝ 4 en termes algébro-géométriques, le théorème de Uhlenbeck–Yau et diverses variantes dûes à Bando et ses collaborateurs. Nous appliquons cette machinerie à la classification des instantons sur certains espaces ALE.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1579

Philippe Eyssidieux 1; Francesco Sala 2

1 Institut Fourier, Université Grenoble-Alpes, Grenoble, France
2 Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Philippe Eyssidieux and Francesco Sala},
     title = {Instantons and framed sheaves on {K\"ahler} {Deligne{\textendash}Mumford} stacks},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {599--628},
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Philippe Eyssidieux; Francesco Sala. Instantons and framed sheaves on Kähler Deligne–Mumford stacks. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 3, pp. 599-628. doi : 10.5802/afst.1579. https://afst.centre-mersenne.org/articles/10.5802/afst.1579/

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