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Recovering the good component of the Hilbert scheme
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2014 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 179, no 3, 805-841 p.Article in journal (Refereed) Published
Abstract [en]

We give an explicit construction, for a flat map X -> S of algebraic spaces, of an ideal in the n'th symmetric product of X over S. Blowing up this ideal is then shown to be isomorphic to the schematic closure in the Hilbert scheme of length n subschemesof the locusof n distinct points.This generalizes Haiman's corresponding result for the affine complex plane.However, our construction of the ideal is very different from that of Haiman, using the formalism of divided powers rather than representation theory.In the nonflat case we obtain a similar result by replacing the n'th symmetric product by the n'th divided power product.

Place, publisher, year, edition, pages
2014. Vol. 179, no 3, 805-841 p.
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URN: urn:nbn:se:kth:diva-145255DOI: 10.4007/annals.2014.179.3.1ISI: 000334404800001ScopusID: 2-s2.0-84897594008OAI: diva2:717614

QC 20140516

Available from: 2014-05-16 Created: 2014-05-15 Last updated: 2014-05-16Bibliographically approved

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