Interpolation on surfaces in $\mathbb {P}^3$
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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 $4$.References
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Additional Information
- Jack Huizenga
- Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02143
- Email: huizenga@math.harvard.edu
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 623-644
- MSC (2010): Primary 14J29; Secondary 14J28, 14J70, 14H50
- DOI: https://doi.org/10.1090/S0002-9947-2012-05582-6
- MathSciNet review: 2995368