Equivalence Relations on Algebraic Curves
Equivalence Relations on Algebraic Curves
复制标题
代数曲线上的等价关系
DOI：
10.2307/1969773
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发表时间：
1952
影响因子：
4.9
通讯作者：
M. Rosenlicht
中科院分区：
文献类型：
--
作者：
M. Rosenlicht
关于把代数曲线上的线性等价的经典理论推广到更一般的等价关系的可能性，人们已经作了许多工作，在这种关系中，所有主因子的群都被某些真子群所代替。Noether的非伴随曲线理论（见本文末尾的参考文献）本质上就是这样一种理论。同样的问题考虑了一些分析家的推广经典雅可比反演定理微分奇异性是在同一个大方向。塞维里最近的“Funzioni准Abeliane”（其中包含一个大的参考书目）包括一个系统的帐户是什么，在我们的语言，是等价关系的曲线与普通的双点和尖点。我们目前的工作涉及代数方面的一般问题，超越事项和广义雅可比簇将在稍后处理。对于所涉及的一般概念，我们参考Zenkiki 1和Chevalley。
Much has been wi-ritten on the possibility of extending the classical theory of linear equivalence on an algebraic curve to more general equivalence relations in which the group of all principle divisors is replaced by certain proper subgroups. Noether's theory of non-adjoint curves (see the end of this paper for references) is essentially a theory of this sort. Similarly the problem considered by a number of analysts of generalizing the classical Jacobi inversion theorem to differentials with singularities is in the same general direction. Severi's recent "Funzioni Quasi Abeliane" (which contains a large bibliography) includes a systematic account of what, in our language, is the equivalence relation on a curve with ordinary double points and cusps. Our present work deals with the algebraic aspects of the general problem; transcendental matters and generalized jacobian varieties will be treated later. For the general concepts involved, we refer to Zariski 1 and Chevalley.