On the Hilbert scheme of points of an almost complex fourfold
type: Item
instance of: scholarly article
title: On the Hilbert scheme of points of an almost complex fourfold
zbMATH Open document ID: 0954.14002
author: Claire Voisin
publication date: 2000-05-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75433
review text: The author proves the following theorem: Let \(X\) be a \(C^\infty\) almost complex fourfold, \(X^{(k)}\) the symmetric power of \(X\), \(X_0^{(k)}\) the open subset of \(k\)-tuples of distinct points. For each \(k\) there exists a manifold \(\text{Hilb}^k(x)\) of real dimension \(4k\) endowed with a stable almost complex structure, and a continuous map \[ c:\text{Hilb}^k(X)\to X^{(k)}, \] which is a diffeomorphism over \(X_0^{(k)}\) and whose fibers over \(z\in X^{(k)}\) are naturally homeomorphic to the fibers of the Hilbert-Chow morphism \(c\) over \(z\) for any almost complex structure on \(X\) integrable in a neighborhood of \(\text{Supp} z\).
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1448503
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: almost complex structure
zbMATH Keywords: pseudoholomorphic curves
zbMATH Keywords: desingularization
zbMATH Keywords: symmetric product
zbMATH Keywords: Hilbert-Chow morphism
reviewed by: S. Ivashkovich
MaRDI profile type: Publication
OpenAlex ID: W2016433438
cites work: Q4895639
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DOI: 10.5802/AIF.1769
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1448503