The number of linear series on curves with given ramification
The number of linear series on curves with given ramification
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具有给定分支的曲线上的线性系列数
DOI：
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发表时间：
2003
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通讯作者：
Brian Osserman
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作者：
Brian Osserman
利用Eisenbud和Harris（1986）的极限线性级数理论，证明了对于特征为0的亏格g的一般光滑曲线，其一般点Pi和指数ei使得Pi（ei − 1）= 2d − 2− g，G1 d（C，{（Pi，ei）}i）是由约化点组成的.我们给出了一个点的数目公式，表明它符合各种已知的特殊情况。我们还猜想一个相应的reducedness结果和公式为g d s的任何尺寸，并减少这三个点的情况下，P，其中一个不再需要考虑模或一般性。
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 P i(ei − 1) = 2d − 2− g, G 1 d (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 g d s of any dimension, and reduce this to the case of three points on P, where one need no longer consider moduli or generality.