### 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) |
---|---|

Pages (from-to) | 623-644 |

Number of pages | 22 |

Journal | Transactions of the American Mathematical Society |

Volume | 365 |

Issue number | 2 |

DOIs | |

State | Published - Nov 30 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Transactions of the American Mathematical Society*, vol. 365, no. 2, pp. 623-644. https://doi.org/10.1090/S0002-9947-2012-05582-6

**Interpolation on surfaces in ℙ ^{3}.** / Huizenga, Jack.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Interpolation on surfaces in ℙ3

AU - Huizenga, Jack

PY - 2012/11/30

Y1 - 2012/11/30

N2 - Suppose S is a surface in ℙ3, and p1,...,pr are general points on S. What is the dimension of the space of sections of OS(e) having singularities of multiplicity mi at pi 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.

AB - Suppose S is a surface in ℙ3, and p1,...,pr are general points on S. What is the dimension of the space of sections of OS(e) having singularities of multiplicity mi at pi 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.

UR - http://www.scopus.com/inward/record.url?scp=84870051468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870051468&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2012-05582-6

DO - 10.1090/S0002-9947-2012-05582-6

M3 - Article

AN - SCOPUS:84870051468

VL - 365

SP - 623

EP - 644

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -