奇异曲线的解析研究
Analytic study of singular curves
摘要：
本文从解析的角度研究了奇异曲线。我们给出了Serre对偶的完全解析证明和一个推广的Abel定理。我们还重新解析地考虑了奇异曲线的Picard簇、Albanese簇和广义Jacobi簇。我们称一个被认为是复李群的Albanese簇为解析Albanese簇。我们详细调查了他们。对于非奇异曲线（紧致Riemann曲面）$X$，其上的亚纯函数场与其Jacobi簇$J(X)$上的亚纯函数场之间存在联系.我们试图将这种关系推广到奇异曲线的情况。
英文摘要：
We study singular curves from analytic point of view. We give completely analytic proofs for the Serre duality and a generalized Abel's theorem. We also reconsider Picard varieties, Albanese varieties and generalized Jacobi varieties of singular curves analytically. We call an Albanese variety considered as a complex Lie group an analytic Albanese variety. We investigate them in detail. For a non-singular curve (a compact Riemann surface) $X$, there is the relation between the meromorphic function fields on $X$ and on its Jacobi variety $J(X)$. We try to extend this relation to the case of singular curves.
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