2016/09/15 by Yukitaka Abe, Abe, Yukitaka · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #math.CV
paper · pdf · doi:10.48550/arxiv.1609.04517
2 figures
openalex publication_date 2016/09/15 · arxiv created 2019/04/08 · arxiv updated 2019/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.