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An intrinsic construction of the principal component of the Hilbert scheme
Department of Mathematics, University of California.ORCID iD: 0000-0003-2505-6417
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2010 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 82, 459-481 p.Article in journal (Refereed) Published
Abstract [en]

The principal component of the Hilbert scheme of n points on a scheme X is the closure of the open subset parameterizing n distinct points. In this article we construct the principal component as a certain blow-up of the symmetric product of X. Our construction is based on a local explicit analysis of etale families, from which the appropriate universal property, needed to identify the principal component with the blow-up, is derived.

Place, publisher, year, edition, pages
2010. Vol. 82, 459-481 p.
Keyword [en]
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URN: urn:nbn:se:kth:diva-26657DOI: 10.1112/jlms/jdq042ISI: 000282175500010ScopusID: 2-s2.0-77957318560OAI: diva2:374195
QC 20101203Available from: 2010-12-03 Created: 2010-11-26 Last updated: 2012-04-14Bibliographically approved

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Rydh, DavidSkjelnes, Roy Mikael
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