## Abstract

Suppose S is a surface in ℙ^{3}, and p1,...,pr are general points on S. What is the dimension of the space of sections of O_{S}(e) having singularities of multiplicity m_{i} at p_{i} for all i? We formulate two natural conjectures which would answer this question, and we show they are equivalent. We then prove these conjectures in case all multiplicities are at most 4.

Original language | English (US) |
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Pages (from-to) | 623-644 |

Number of pages | 22 |

Journal | Transactions of the American Mathematical Society |

Volume | 365 |

Issue number | 2 |

DOIs | |

State | Published - 2012 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- Applied Mathematics

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