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Infinite intersections of open subschemes and the Hilbert scheme of points

โœ Scribed by Roy M. Skjelnes; Charles Walter

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
234 KB
Volume
273
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We study infinite intersections of open subschemes and the corresponding infinite intersection of Hilbert schemes. If {U ฮฑ } 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,P ) = ฮฑ U ฮฑ is given by the infinite intersection ฮฑ Hilb U ฮฑ , where Hilb U ฮฑ is the Hilbert functor of flat and finite families on U ฮฑ . In particular, we show that the Hilbert functor of flat and finite families on Spec(O X,P ) is representable by a scheme.

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