Title | **Generic initial ideals of points and curves** |

Author(s) | Aldo Conca, Jessica Sidman |

Type | Article in Journal |

Abstract | Let I be the defining ideal of a smooth complete intersection space curve C with defining equations of degrees a and b . We use the partial elimination ideals introduced by Mark Green to show that the lexicographic generic initial ideal of I has Castelnuovo–Mumford regularity 1 + a b ( a − 1 ) ( b − 1 ) / 2 with the exception of the case a = b = 2 , where the regularity is 4. Note that a b ( a − 1 ) ( b − 1 ) / 2 is exactly the number of singular points of a general projection of C to the plane. Additionally, we show that for any term ordering τ , the generic initial ideal of a generic set of points in P r is a τ -segment ideal. |

Keywords | Generic initial ideal, Curves, Points, Lexicographic term order |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717105000714 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 40 |

Number | 3 |

Pages | 1023 - 1038 |

Year | 2005 |

Edition | 0 |

Translation |
No |

Refereed |
No |