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Compactifying locally Cohen-Macaulay projective curvesHønsen, Morten January 2005 (has links)
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. / QC 20101022
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Compactifying locally Cohen-Macaulay projective curvesHønsen, Morten January 2005 (has links)
<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>
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The design and implementation of an applet to simulate curved spaceErickson, Stephanie Jeanne. January 2010 (has links)
Honors Project--Smith College, Northampton, Mass., 2010. / Includes bibliographical references (p. 42).
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