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PROPER HOLOMORPHIC MAPPINGS ONTO SYMMETRIC PRODUCTS OF A RIEMANN SURFACE

Bharali, Gautam and Biswas, Indranil and Divakaran, Divakaran and Janardhanan, Jaikrishnan (2018) PROPER HOLOMORPHIC MAPPINGS ONTO SYMMETRIC PRODUCTS OF A RIEMANN SURFACE. In: DOCUMENTA MATHEMATICA, 23 . pp. 1291-1311.

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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: Journal Article
Additional Information: copyright for this article belongs to the authors
Keywords: Proper holomorphic maps; Riemann surfaces; symmetric product; taut manifolds
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 17 Jul 2019 06:58
Last Modified: 17 Jul 2019 06:58
URI: http://eprints.iisc.ac.in/id/eprint/62904

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