The Canonical Model of a Singular Curve
We give re fined statements and modern proofs of Rosenlicht's re- sults about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equ...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Springer
2011
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| Online Access: | http://hdl.handle.net/1721.1/62837 https://orcid.org/0000-0001-7331-0761 |
| _version_ | 1811093215554568192 |
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| author | Kleiman, Steven L. Vidal Martins, Renato |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kleiman, Steven L. Vidal Martins, Renato |
| author_sort | Kleiman, Steven L. |
| collection | MIT |
| description | We give re fined statements and modern proofs of Rosenlicht's re-
sults about the canonical model C′ of an arbitrary complete integral curve C.
Notably, we prove that C and C′ are birationally equivalent if and only if C
is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal to the
blowup of C with respect to the canonical sheaf [omega]. We also prove some new
results: we determine just when C′ is rational normal, arithmetically normal,
projectively normal, and linearly normal. |
| first_indexed | 2024-09-23T15:41:29Z |
| format | Article |
| id | mit-1721.1/62837 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:41:29Z |
| publishDate | 2011 |
| publisher | Springer |
| record_format | dspace |
| spelling | mit-1721.1/628372022-09-29T15:31:03Z The Canonical Model of a Singular Curve Kleiman, Steven L. Vidal Martins, Renato Massachusetts Institute of Technology. Department of Mathematics Kleiman, Steven L. Kleiman, Steven L. We give re fined statements and modern proofs of Rosenlicht's re- sults about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal to the blowup of C with respect to the canonical sheaf [omega]. We also prove some new results: we determine just when C′ is rational normal, arithmetically normal, projectively normal, and linearly normal. Conselho Nacional de Pesquisas (Brazil) (Grant number PDE 200999/2005-2) 2011-05-18T21:06:22Z 2011-05-18T21:06:22Z 2009-04 2008-03 Article http://purl.org/eprint/type/JournalArticle 0046-5755 http://hdl.handle.net/1721.1/62837 Kleiman, Steven Lawrence, and Renato Vidal Martins. “The canonical model of a singular curve.” Geometriae Dedicata 139.1 (2009) : 139-166. Copyright © 2009, Springer https://orcid.org/0000-0001-7331-0761 en_US http://dx.doi.org/10.1007/s10711-008-9331-4 Geometriae Dedicata Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Springer Prof. Kleiman via Michael Noga |
| spellingShingle | Kleiman, Steven L. Vidal Martins, Renato The Canonical Model of a Singular Curve |
| title | The Canonical Model of a Singular Curve |
| title_full | The Canonical Model of a Singular Curve |
| title_fullStr | The Canonical Model of a Singular Curve |
| title_full_unstemmed | The Canonical Model of a Singular Curve |
| title_short | The Canonical Model of a Singular Curve |
| title_sort | canonical model of a singular curve |
| url | http://hdl.handle.net/1721.1/62837 https://orcid.org/0000-0001-7331-0761 |
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