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arXiv · 1609.04517

Analytic study of singular curves

Yukitaka Abe
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Abstract

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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Yukitaka Abe. 2016-09-15. Analytic study of singular curves. https://arxiv.org/abs/1609.04517

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