Title | **New effective bounds on the dimension of a linear system in** |

Author(s) | Marcin Dumnicki, Witold Jarnicki |

Type | Article in Journal |

Abstract | The main goal of this paper is to present an algorithm bounding the dimension of a linear system of plane curves of given degree (or monomial basis) with multiple points in general position. As a result we prove the Harbourne–Hirschowitz conjecture when the multiplicities of base points are bounded by 11. This gives a partial answer to the question of when bivariate polynomial interpolation is possible. |

Keywords | Harbourne–Hirschowitz conjecture, Zero-dimensional schemes, Gröbner bases |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717107000120 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 42 |

Number | 6 |

Pages | 621 - 635 |

Year | 2007 |

Edition | 0 |

Translation |
No |

Refereed |
No |