Linear series over real and p-adic fields
Linear series over real and p-adic fields
复制标题
实数域和 p 进数域上的线性级数
DOI：
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发表时间：
2005
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通讯作者：
Brian Osserman
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作者：
Brian Osserman
我们注意到，作者在2003年给出的退化参数导出了从亏格g到P1的一般曲线C的映射的个数公式，当在真实的数或p-adic域上工作时，也得到了较弱的结果.具体地说，设k是这样一个域：我们看到给定g，d，n和e 1，.当满足ε i（ei-1）= 2d - 2 - g时，存在亏格为g的光滑曲线C和点P1，...，P n，使得从C到P 1的所有映射，直到图像的自同构，都可以定义在k上。我们还注意到，类似的结果将遵循从地图到高维射影空间，如果它是证明的情况下C = P 1，n = 3，并感谢工作的Sottile，无条件的结果可能会获得特殊的分歧条件。
We note that the degeneration arguments given by the author in 2003 to derive a formula for the number of maps from a general curve C of genus g to P 1 with prescribed ramification also yields weaker results when working over the real numbers or p-adic fields. Specifically, let k be such a field: we see that given g, d, n, and e 1 ,..e n satisfying Σ ι (e i -1) = 2d - 2 - g, there exists smooth curves C of genus g together with points P 1 ,..., P n such that all maps from C to P 1 can, up to automorphism of the image, be defined over k. We also note that the analagous result will follow from maps to higher-dimensional projective spaces if it is proven in the case C = P 1 , n = 3, and that thanks to work of Sottile, unconditional results may be obtained for special ramification conditions.