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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiple points in $ \mathbf{P}^2$ and degenerations to elliptic curves


Author: Ivan Petrakiev
Journal: Proc. Amer. Math. Soc. 137 (2009), 65-71
MSC (2000): Primary 14C20; Secondary 14N05
Published electronically: August 15, 2008
MathSciNet review: 2439426
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Abstract: We consider the problem of bounding the dimension of the linear system of curves in $ \mathbf{P}^2$ of degree $ d$ with prescribed multiplicities $ m_1,\dots,m_n$ at $ n$ general points (Harbourne (1986), Hirschowitz (1985)). We propose a new method, based on the work of Ciliberto and Miranda (2000, 2003), by specializing the general points to an elliptic curve in $ \mathbf{P}^2$.


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Additional Information

Ivan Petrakiev
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: igp@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09540-3
PII: S 0002-9939(08)09540-3
Received by editor(s): August 22, 2006
Received by editor(s) in revised form: July 19, 2007, and December 28, 2007
Published electronically: August 15, 2008
Additional Notes: The author was partially supported by an NSF Graduate Research Fellowship.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society