On the fiber product over infinite-genus Riemann surfaces

2022/10/07 by John A. Arredondo, Arredondo, John A., Saúl Quispe +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #General Topology (math.GN) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2210.03605

openalex publication_date 2022/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Considering non-constant holomorphic maps β_i:S_i→ S₀, i∈\1,2\, between non-compact Riemann surfaces for which it is associated its fiber product S₁×_(β₁,β₂)S₂. With this setting, in this paper we relate the ends space of such fiber product to the ends space of its normal fiber product. Moreover, we provide conditions on the maps β₁ and β₂ to guarantee connectednes on the fiber product. From these conditions, we link the ends space of fiber product with the topological type of the Riemann surfaces S₁ and S₂. We also study the fiber product over infinite hyperelliptic curves and discuss its connectedness and ends space.

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