Finiteness Theorems for Products and Symmetric Products of Hyperbolic Riemann Surfaces

2016/12/07 by Divakaran Divakaran, Divakaran, Divakaran, Jaikrishnan Janardhanan +1
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1612.02121

openalex publication_date 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if X = X₁ × … × X_n is a product of hyperbolic Riemann surfaces of finite type and Y = Ω/Γ is a complex manifold, where Ω is a bounded simply-connected domain in ℂ^m, then the space of dominant holomorphic mappings from X to Y is a finite set. As corollaries, we obtain the finiteness of the space of dominant holomorphic mappings into products and symmetric products of hyperbolic Riemann surfaces.

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