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 |
|---|---|
| Publication: | DOCUMENTA MATHEMATICA |
| Publisher: | FIZ KARLSRUHE-LEIBNIZ-INST INFORMATIONSINFRASTRUKTUR |
| 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 |
| 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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