I'm studying the Hilbert scheme of points on a surface and I've just defined the set-theoretic Hilbert-Chow morphism. I would like to know if someone knows a reference to study the scheme-theoretic construction of the Hilbert-Chow morphism. I was suggested to search an article of Lehn, but all his articles, I've seen, never talk about that. Thank you!
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1$\begingroup$ One source is 'Local properties and Hilbert schemes of points' by Fantechi and Göttsche, in the volume 'Fundamental Algebraic Geometry' for the 2003 Trieste School, published by AMS. $\endgroup$– Matthieu RomagnyCommented Jul 4, 2014 at 16:12
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$\begingroup$ Matthieu's suggestion is excellent. Another reference is Section I.6 of Koll'ar's "Rational Curves on Algebraic Varieties". $\endgroup$– Jason StarrCommented Jul 4, 2014 at 17:51
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1$\begingroup$ See Amnon Neeman, Zero cycles in $P^n$, Adv. Math. 89 (1991), no. 2, 217–227. There is also a discussion in Section 4.3 of David Rydh's paper Hilbert and Chow schemes, symmetric powers and divided powers, math.kth.se/~dary/thesis/thesis-paperIII.pdf $\endgroup$– ACLCommented Jul 4, 2014 at 20:42
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