Stanford Algebraic Geometry — Seminar — LINEAR SYSTEMS OF PLANE CURVES WITH BASE POINTS OF BOUNDED MULTIPLICITY
نویسنده
چکیده
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 base locus. We discuss different approaches for attacking this conjecture, and show that it holds for all systems with base points of multiplicity 7 or less. Friday, March 4 3:30 p.m., after the kiddie colloquium (Note unusual time!) Room 383-N http://math.stanford.edu/~vakil/s0405/
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