Let C⊆Prk be a non-degenerate projective curve of degree r+2, where r≥3. By means of the Hartshorne-Rao module of C we distinguish 4 different possible cases (and an exceptional case which only appears if r=3). In any case C is obtained either by means of an embedding of an arbitrary smooth curve C0 of genus 2, or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions of the homogeneous coordinate ring of C are studied. © 2001 Academic Press.

Brodmann, M; Schenzel, P (2001). *Curves of degree r + 2 in ℙr: Cohomological, geometric, and homological aspects.* Journal of Algebra, 242(2):577-623.

## Abstract

Let C⊆Prk be a non-degenerate projective curve of degree r+2, where r≥3. By means of the Hartshorne-Rao module of C we distinguish 4 different possible cases (and an exceptional case which only appears if r=3). In any case C is obtained either by means of an embedding of an arbitrary smooth curve C0 of genus 2, or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions of the homogeneous coordinate ring of C are studied. © 2001 Academic Press.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | Betti numbers; Castelnuovo regularity; Elliptic normal curve; Hartshorne-Rao module; Projective curves; Rational normal curve; Surface of minimal degree |

Language: | English |

Date: | 2001 |

Deposited On: | 27 May 2010 16:29 |

Last Modified: | 05 Apr 2016 13:25 |

Publisher: | Elsevier |

ISSN: | 0021-8693 |

Publisher DOI: | https://doi.org/10.1006/jabr.2001.8847 |

Related URLs: | http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1031.14013 |

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