Hilbert-Chow morphism

Theorem 1.1.7 [Mumford-Fogarty (1) 5.4]. There is a canonical morphism (the Hilbert Chow morphism)... 

This morphism vr is called the Hilbert-Chow morphism which associates a closed subscheme with its corresponding cycle. For example, Oxj J is mapped to 2[x in the... 

Theorem 4.1 (Ginzburg and Kapranov [25], Y. Ito and I. Nakamura [42]). The re striction of the Hilbert-Chow morphism to X is the minimal resolution of singularities... 

Let 7t S "(C ) be the Hilbert-Chow morphism. In Chapter 1, we have shown... 

As remarked above, we may define the unstable manifold W of the fixed point set A E for the total space of a holomorphic line bundle over E. More generally, let X be a surface containing a curve E. By identifying a tubular neighborhood of E with the total space of the normal bundle of E in X, we can define the unstable manifold W. In fact, this can be defined intrinsically as follows. Let tt X "] S "X be the Hilbert-Chow morphism. We define... 

Definition 2.4.1. Let S be a smooth projective variety over an algebraically closed field. Let as above —> S be the Hilbert-Chow morphism. Let... 

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