A compact moduli space for Cohen-Macaulay curves in projective space
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
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| Format: | Thesis |
| Language: | en_US |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/28826 |
| _version_ | 1826197353099427840 |
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| author | Hønsen, Morten Oskar, 1973- |
| author2 | Aise Johan de Jong. |
| author_facet | Aise Johan de Jong. Hønsen, Morten Oskar, 1973- |
| author_sort | Hønsen, Morten Oskar, 1973- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. |
| first_indexed | 2024-09-23T10:46:23Z |
| format | Thesis |
| id | mit-1721.1/28826 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:46:23Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/288262019-04-10T21:27:08Z A compact moduli space for Cohen-Macaulay curves in projective space Hønsen, Morten Oskar, 1973- Aise Johan de Jong. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. Includes bibliographical references (p. 57-59). 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 of this thesis is that our functor is represented by a proper algebraic space. As an application we obtain 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. by Morten Oskar Hønsen. Ph.D. 2005-09-27T18:33:32Z 2005-09-27T18:33:32Z 2004 2004 Thesis http://hdl.handle.net/1721.1/28826 60351837 en_US M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 59 p. 2324962 bytes 2330137 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Hønsen, Morten Oskar, 1973- A compact moduli space for Cohen-Macaulay curves in projective space |
| title | A compact moduli space for Cohen-Macaulay curves in projective space |
| title_full | A compact moduli space for Cohen-Macaulay curves in projective space |
| title_fullStr | A compact moduli space for Cohen-Macaulay curves in projective space |
| title_full_unstemmed | A compact moduli space for Cohen-Macaulay curves in projective space |
| title_short | A compact moduli space for Cohen-Macaulay curves in projective space |
| title_sort | compact moduli space for cohen macaulay curves in projective space |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/28826 |
| work_keys_str_mv | AT hønsenmortenoskar1973 acompactmodulispaceforcohenmacaulaycurvesinprojectivespace AT hønsenmortenoskar1973 compactmodulispaceforcohenmacaulaycurvesinprojectivespace |