A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
In this article we address the problem of computing the dimension of the space of plane curves of degree d with n general points of multiplicity m. A conjecture of Harbourne and Hirschowitz implies that when d ≥ 3m, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing a multiple (−1)-curve. We reformulate this conjecture by explicitly listing those systems which havedoi:10.1090/s0002-9947-00-02416-8 fatcat:iojv2dh2vfco3cz7aaanqvszfm