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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiple points in $\mathbf {P}^2$ and degenerations to elliptic curves
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by Ivan Petrakiev
Proc. Amer. Math. Soc. 137 (2009), 65-71
DOI: https://doi.org/10.1090/S0002-9939-08-09540-3
Published electronically: August 15, 2008

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 $\mathbf {P}^2$.
References
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Bibliographic Information
  • Ivan Petrakiev
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email: igp@umich.edu
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 65-71
  • MSC (2000): Primary 14C20; Secondary 14N05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09540-3
  • MathSciNet review: 2439426