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Compactifying locally Cohen-Macaulay projective curves

<p>We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most important is that the map is almost everywhere an isomorphism onto its image. The motivation for this definition comes from trying to interpolate between the Hilbert scheme and the Kontsevich mapping space. The main result is that our functor is represented by a proper algebraic space. As applications we obtain a new proof of the existence of Macaulayfications for varieties, and secondly, interesting compactifications of the spaces of smooth curves in projective space. We illustrate this in the case of rational quartics, where the resulting space appears easier than the Hilbert scheme.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:kth-470
Date January 2005
CreatorsHønsen, Morten
PublisherKTH, Mathematics (Dept.), Stockholm : Matematik
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeDoctoral thesis, monograph, text

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