### Abstract

Let C ⊂ ℙ^{r} be a linearly normal projective integral curve of arithmetic genus g ≥ 1 and degree d = 2g + 1 + p for some p ≥ 1. It is well known that C is cut out by quadric and satisfies Green-Lazarsfeld's property N_{p}. Recently it is known that for any q ∈ ℙ^{r}\C such that the linear projection π_{q}: C → ℙ^{r-1} of C from q is an embedding, the projected image C_{q}:= π_{q}(C) ⊂ ℙ^{r-1} is 3-regular, and hence its homogeneous ideal is generated by quadratic and cubic equations. In this article we study the problem when C_{q} is still cut out by quadrics. Our main result in this article shows that if the relative location of q with respect to C is general then the homogeneous ideal of C _{q} is still generated by quadrics and the syzygies among them are generated by linear syzygies for the first a few steps.

Original language | English |
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Pages (from-to) | 2092-2099 |

Number of pages | 8 |

Journal | Communications in Algebra |

Volume | 41 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2013 May 1 |

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### Keywords

- Linear projection
- Minimal free resolution
- Projective curve

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*41*(6), 2092-2099. https://doi.org/10.1080/00927872.2011.653464