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Infinite intersections of open subschemes and the Hilbert scheme of points
KTH, Superseded Departments, Mathematics.
2004 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 273, no 2, 571-585 p.Article in journal (Refereed) Published
Abstract [en]

We study infinite intersections of open subschemes and the corresponding infinite intersection of Hilbert schemes. If {U-alpha} is the collection of open subschemes of a variety X containing the fixed point P, then we show that the Hilbert functor of flat and finite families of Spec(O-X,O- P) = boolean AND(alpha) U-alpha is given by the infinite intersection boolean AND(alpha) Hilb(Ualpha), where Hilb(Ualpha), is the Hilbert functor of flat and finite families on U-alpha. In particular, we show that the Hilbert functor of flat and finite families on Spec(O-X,O- P) is representable by a scheme.

Place, publisher, year, edition, pages
2004. Vol. 273, no 2, 571-585 p.
Keyword [en]
infinite intersection, Hilbert schemes, localized schemes, determinants, line
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23186DOI: 10.1016/s0021-8693(03)00495-2ISI: 000189079300008Scopus ID: 2-s2.0-1442307651OAI: oai:DiVA.org:kth-23186DiVA: diva2:341884
Note
QC 20100525 QC 20111027Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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  • nn-NB
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  • Other locale
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  • asciidoc
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