### Abstract

In this article we study nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay. Note that for a rational normal curve and a point. Our main result is about the relation between the geometric properties of X and the position of P with respect to We show that the graded Betti numbers of X are uniquely determined by the rank of P with respect to. In particular, X satisfies property N _{2,p} if and only if. Therefore property N _{2,p} of X is controlled by and conversely can be read off from the minimal free resolution of X. This result provides a non-linearly normal example for which the converse to Theorem 1.1 in (Eisenbud et al., Compositio Math 141:1460-1478, 2005) holds. Also our result implies that for nondegenerate projective curves of degree d which are not arithmetically Cohen-Macaulay, there are exactly distinct Betti tables.

Original language | English |
---|---|

Pages (from-to) | 685-697 |

Number of pages | 13 |

Journal | Mathematische Zeitschrift |

Volume | 256 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Jul 1 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Projective curves of degree=codimension+2'. Together they form a unique fingerprint.

## Cite this

*Mathematische Zeitschrift*,

*256*(3), 685-697. https://doi.org/10.1007/s00209-007-0101-z