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

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

2004-06-29

arxiv.org/abs/math/0406591v3

J. Algebraic Geom. 16 (2007), 19-38

Mathematics

Algebraic Geometry

No major changes. Fixed about a dozen typos and updated journal information

Scientific paper

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.

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