Multiple points in 𝐏² and degenerations to elliptic curves

Petrakiev, Ivan

doi:10.1090/S0002-9939-08-09540-3

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

Proc. Amer. Math. Soc. 137 (2009), 65-71 Request permission

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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