Nous donnons une généralisation champêtre de résultats classiques de théorie de jauge, comme la caractérisation par Donaldson des instantons sur 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.
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.
@article{AFST_2018_6_27_3_599_0, 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}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 27}, number = {3}, year = {2018}, doi = {10.5802/afst.1579}, zbl = {06979712}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1579/} }
TY - JOUR AU - Philippe Eyssidieux AU - Francesco Sala TI - Instantons and framed sheaves on Kähler Deligne–Mumford stacks JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2018 SP - 599 EP - 628 VL - 27 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1579/ DO - 10.5802/afst.1579 LA - en ID - AFST_2018_6_27_3_599_0 ER -
%0 Journal Article %A Philippe Eyssidieux %A Francesco Sala %T Instantons and framed sheaves on Kähler Deligne–Mumford stacks %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2018 %P 599-628 %V 27 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1579/ %R 10.5802/afst.1579 %G en %F AFST_2018_6_27_3_599_0
Philippe Eyssidieux; Francesco Sala. Instantons and framed sheaves on Kähler Deligne–Mumford stacks. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 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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