Proper holomorphic mappings onto symmetric products of a Riemann surface

Bharali, Gautam and Biswas, Indranil and D, Divakaran and Jaikrishnan, Janardhanan (2018) Proper holomorphic mappings onto symmetric products of a Riemann surface. Documenta Mathematica. pp. 1-16.

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Abstract

We show that the structure of proper holomorphic maps between the n -fold symmetric products, n≥2 , of a pair of non-compact Riemann surfaces X and Y , provided these are reasonably nice, is very rigid. Specifically, any such map is determined by a proper holomorphic map of X onto Y . This extends existing results concerning bounded planar domains, and is a non-compact analogue of a phenomenon observed in symmetric products of compact Riemann surfaces. Along the way, we also provide a condition for the complete hyperbolicity of all n -fold symmetric products of a non-compact Riemann surface.

Item Type:	Article
Authors:	Bharali, Gautam and Biswas, Indranil and D, Divakaran and Jaikrishnan, Janardhanan
Document Language:	Language English
Uncontrolled Keywords:	Mathematics - Complex Variables; Mathematics - Algebraic Geometry; 14J50; 32H35 (Primary) 32Q45 (Secondary)
Subjects:	Natural Sciences > Mathematics
Divisions:	Azim Premji University - Bengaluru
Full Text Status:	Public
Related URLs:	Publisher
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/4359
Publisher URL:

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