Interpolation on surfaces in ℙ3

Jack Huizenga

doi:10.1090/S0002-9947-2012-05582-6

Interpolation on surfaces in ℙ³

Jack Huizenga

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 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	https://doi.org/10.1090/S0002-9947-2012-05582-6
State	Published - 2012

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-2012-05582-6

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title = "Interpolation on surfaces in ℙ3",

abstract = "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.",

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AU - Huizenga, Jack

PY - 2012

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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 - https://www.scopus.com/pages/publications/84870051468

UR - https://www.scopus.com/pages/publications/84870051468#tab=citedBy

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

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

M3 - Article

AN - SCOPUS:84870051468

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VL - 365

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EP - 644

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

Interpolation on surfaces in ℙ³

Abstract

All Science Journal Classification (ASJC) codes

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