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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The fat locus of Hilbert schemes of points


Author: Marc Coppens
Journal: Proc. Amer. Math. Soc. 118 (1993), 777-783
MSC: Primary 14C05; Secondary 14E40
MathSciNet review: 1145416
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Abstract: Let $ X$ be a smooth projective variety over an algebraically closed field $ k$. Let $ {\operatorname{Hilb} ^d}(X)$ be its Hilbert scheme of 0-dimensional subschemes of $ X$ of degree $ d$. Let $ [{\operatorname{Hilb} ^d}(X)](k)$ be the set of $ k$-rational points. We prove that the subset of points of $ [{\operatorname{Hilb} ^d}(X)](k)$ corresponding to fat points on $ X$ is a locally closed subset with respect to the Zariski topology.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1145416-X
PII: S 0002-9939(1993)1145416-X
Article copyright: © Copyright 1993 American Mathematical Society