Linear Systems in P2 with Base Points of Bounded Multiplicity
نویسنده
چکیده
We present a proof of the Harbourne-Hirschowitz conjecture for linear systems with multiple points of order 7 or less. This uses a well-known degeneration of the plane developed by Ciliberto and Miranda as well as a combinatorial game that arises from specializing points onto lines.
منابع مشابه
Stanford Algebraic Geometry — Seminar — LINEAR SYSTEMS OF PLANE CURVES WITH BASE POINTS OF BOUNDED MULTIPLICITY
We address the problem of computing the dimension of the space of plane curves of fixed degree and general multiple base points. A conjecture of Harbourne and Hirschowitz gives geometric meaning to when this dimension is larger than the expected dimension obtained from Riemann-Roch; specifically, the dimension is larger than expected if and only if the system has a multiple (−1)-curve in its ba...
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تاریخ انتشار 2009