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Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation
[Espaces de modules de faisceaux semistables par rapport à une polarisation kählérienne]
Daniel Greb1 ; Matei Toma2
1 Essener Seminar für Algebraische Geometrie und Arithmetik, Fakultät für Mathematik, Universität Duisburg–Essen 45112 Essen, Germany
2 Université de Lorraine, CNRS, IECL F-54000 Nancy, France
Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 233-261.

En utilisant le critère d’existence d’un bon espace de modules d’un champ d’Artin dû à Alper–Fedorchuk–Smyth, nous construisons un espace de modules propre de faisceaux de rang 2 sur une variété projective complexe donnée, de classes de Chern fixées et qui sont Gieseker-Maruyama-semistables par rapport à une classe de Kähler fixée.

Using an existence criterion for good moduli spaces of Artin stacks by Alper–Fedorchuk–Smyth we construct a proper moduli space of rank two sheaves with fixed Chern classes on a given complex projective manifold that are Gieseker-Maruyama-semistable with respect to a fixed Kähler class.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.116
Classification : 32G13, 14D20, 14D23, 14J60
Keywords: Kähler manifolds, moduli of coherent sheaves, algebraic stacks, good moduli spaces, semi-universal deformations, local quotient presentations
Mot clés : Variétés de Kähler, modules de faisceaux cohérents, champs algébriques, bons espaces de modules, déformations semi-universelles, présentations quotient locales
Daniel Greb 1 ; Matei Toma 2

1 Essener Seminar für Algebraische Geometrie und Arithmetik, Fakultät für Mathematik, Universität Duisburg–Essen 45112 Essen, Germany
2 Université de Lorraine, CNRS, IECL F-54000 Nancy, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Daniel Greb; Matei Toma. Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation. Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 233-261. doi : 10.5802/jep.116. https://jep.centre-mersenne.org/articles/10.5802/jep.116/

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