An intrinsic construction of the principal component of the Hilbert scheme
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
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.
FAMILIES, POINTS, POWERS
IdentifiersURN: urn:nbn:se:kth:diva-26657DOI: 10.1112/jlms/jdq042ISI: 000282175500010ScopusID: 2-s2.0-77957318560OAI: oai:DiVA.org:kth-26657DiVA: diva2:374195
QC 201012032010-12-032010-11-262012-04-14Bibliographically approved