On the Hilbert scheme of points of an almost complex fourfold
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 \(\text{Supp} z\).
scientific article; zbMATH DE number 1448503