## 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
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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 $\mathbf {P}^2$.## 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