On the Hilbert scheme of points of an almost complex fourfold
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, p. 689-722

If S is a complex surface, one has for each k the Hilbert scheme Hilb k (S), which is a desingularization of the symmetric product S (k) . Here we construct more generally a differentiable variety Hilb k (X) endowed with a stable almost complex structure, for every almost complex fourfold X. Hilb k (X) is a desingularization of the symmetric product X (k) .

Si S est une surface complexe, on peut définir pour chaque entier k le schéma de Hilbert Hilb k (S), qui est une désingularisation du produit symétrique S (k) . On construit ici plus généralement une variété différentiable Hilb k (X) munie d’une structure presque complexe stable, pour toute variété différentiable X de dimension 4 munie d’une structure presque complexe. Hilb k (X) est une désingularisation du produit symétrique X (k) .

@article{AIF_2000__50_2_689_0,
     author = {Voisin, Claire},
     title = {On the Hilbert scheme of points of an almost complex fourfold},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     pages = {689-722},
     doi = {10.5802/aif.1769},
     zbl = {0954.14002},
     mrnumber = {2001k:32048},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2000__50_2_689_0}
}
Voisin, Claire. On the Hilbert scheme of points of an almost complex fourfold. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 689-722. doi : 10.5802/aif.1769. http://www.numdam.org/item/AIF_2000__50_2_689_0/

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