Geodesic
Proper Holomorphic Mappings onto Symmetric Products of a Riemann Surface
Documenta mathematica, Tome 23 (2018), pp. 1291-1311
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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.
DOI : 10.4171/dm/648
Classification : 30F99, 32H35
Mots-clés : Riemann surfaces, symmetric product, proper holomorphic maps 
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     author = {Gautam Bharali and Divakaran Divakaran and Jaikrishnan Janardhanan and Indranil Biswas},
     title = {Proper {Holomorphic} {Mappings} onto {Symmetric} {Products} of a {Riemann} {Surface}},
     journal = {Documenta mathematica},
     pages = {1291--1311},
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     volume = {23},
     doi = {10.4171/dm/648},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/648/}
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Gautam Bharali; Divakaran Divakaran; Jaikrishnan Janardhanan; Indranil Biswas. Proper Holomorphic Mappings onto Symmetric Products of a Riemann Surface. Documenta mathematica, Tome 23 (2018), pp. 1291-1311. doi: 10.4171/dm/648

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