Abstract
We use Eisenbud and Harris' theory of limit linear series (1986) to show that for a general smooth curve of genus g in characteristic 0, with general points Pi and indices ei such that ∑i(ei−1)=2d−2−g, Gd1 (C,{(Pi,ei)}i) is made up of reduced points. We give a formula for the number of points, showing that it agrees with various known special cases. We also conjecture a corresponding reducedness result and formula for gdr's of any dimension, and reduce this to the case of three points on ℙ1, where one needs no longer consider moduli or generality.
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