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 ${\mathrm{Hilb}}^{k}\left(S\right)$, which is a desingularization of the symmetric product ${S}^{\left(k\right)}$. Here we construct more generally a differentiable variety ${\mathrm{Hilb}}^{k}\left(X\right)$ endowed with a stable almost complex structure, for every almost complex fourfold $X$. ${\mathrm{Hilb}}^{k}\left(X\right)$ is a desingularization of the symmetric product ${X}^{\left(k\right)}$.

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

@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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