Multiple points in P² and degenerations to elliptic curves

2004/03/26 by Petrakiev, Ivan
#14C20 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0403464

Abstract

We consider the problem of bounding the dimension of the linear system of curves in \bf P² of degree d with prescribed multiplicities m₁,...,m_n at n general points (\citeHir1,\citeHir2). 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 P².

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