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Multiple points in P^2 and degenerations to elliptic curves

Ivan Petrakiev
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Abstract

We consider the problem of bounding the dimension of the linear system of curves in ${\bf P}^2$ of degree $d$ with prescribed multiplicities $m_1,...,m_n$ at $n$ general points (\cite{Hir1},\cite{Hir2}). We propose a new method, based on the work of Ciliberto and Miranda (\cite {CM1}, \cite {CM2}), by specializing the general points to an elliptic curve in ${\bf P}^2$.

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Ivan Petrakiev. 2006-04-24. Multiple points in P^2 and degenerations to elliptic curves. https://arxiv.org/abs/math/0403464

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