# Linear systems in $\mathbb{P}^2$ with base points of bounded multiplicity

@article{Yang2004LinearSI,
title={Linear systems in \$\mathbb\{P\}^2\$ with base points of bounded multiplicity},
author={Stephanie Yang},
journal={Journal of Algebraic Geometry},
year={2004},
volume={16},
pages={19-38}
}
• Stephanie Yang
• Published 29 June 2004
• Mathematics
• Journal of Algebraic Geometry
We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with base points of multiplicity seven or less. This proof uses a well-known degeneration of the projective plane, as well as a combinatorial technique that arises from specializing points onto a line.
14 Citations

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## References

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In this article we address the problem of computing the dimenlsion of the space of plane curves of degree d with n general points of multiplicity m. A conjecture of Harbourne and Hirschowitz implies
A linear system of plane curves satisfying multiplicity conditions at points in general position is called special if the dimension is larger than the expected dimension. A (−1) curve is an
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An approach is proposed based on an analysis of the corresponding linear system on a degeneration of the plane itself, leading to a simple recursion for these dimensions, obtaining results in the quasi-homogeneous'' case when all the multiplicities are equal except one.
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0. Introduction. Soient pl5..., pr des points suffisamment generaux (ou generiques) du plan projectif et ml9 ..., mr des entiers positifs. Quelle est la dimension du Systeme lineaire des courbes