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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolation on surfaces in $ \mathbb{P}^3$


Author: Jack Huizenga
Journal: Trans. Amer. Math. Soc. 365 (2013), 623-644
MSC (2010): Primary 14J29; Secondary 14J28, 14J70, 14H50
Published electronically: August 30, 2012
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Abstract: Suppose $ S$ is a surface in $ \mathbb{P}^3$, and $ p_1,\ldots ,p_r$ are general points on $ S$. What is the dimension of the space of sections of $ \mathcal {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$.


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Additional Information

Jack Huizenga
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02143
Email: huizenga@math.harvard.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05582-6
PII: S 0002-9947(2012)05582-6
Received by editor(s): August 27, 2010
Received by editor(s) in revised form: January 2, 2011, and January 24, 2011
Published electronically: August 30, 2012
Additional Notes: This material is based upon work supported under a National Science Foundation Graduate Research Fellowship
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.