[Espaces de modules de faisceaux semistables par rapport à une polarisation kählérienne]
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 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.
Accepté le :
Publié le :
DOI : 10.5802/jep.116
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
CC-BY 4.0
@article{JEP_2020__7__233_0,
author = {Daniel Greb and Matei Toma},
title = {Moduli spaces of sheaves that are semistable with respect to a {K\"ahler} polarisation},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {233--261},
publisher = {\'Ecole polytechnique},
volume = {7},
year = {2020},
doi = {10.5802/jep.116},
zbl = {07152736},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.116/}
}
TY - JOUR AU - Daniel Greb AU - Matei Toma TI - Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation JO - Journal de l’École polytechnique — Mathématiques PY - 2020 SP - 233 EP - 261 VL - 7 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.116/ DO - 10.5802/jep.116 LA - en ID - JEP_2020__7__233_0 ER -
%0 Journal Article %A Daniel Greb %A Matei Toma %T Moduli spaces of sheaves that are semistable with respect to a Kähler polarisation %J Journal de l’École polytechnique — Mathématiques %D 2020 %P 233-261 %V 7 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.116/ %R 10.5802/jep.116 %G en %F JEP_2020__7__233_0
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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