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A note on planarity stratication of Hurwitz spaces
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2015 (English)In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 58, no 3, 596-609 p.Article in journal (Refereed) Published
Abstract [en]

One can easily show that any meromorphic function on a complex closed Riemann surface  can be represented as a composition of a birational map of this surface to $\CP^2$  and  a  projection of the image curve  from an appropriate point $p\in \CP^2$ to the pencil of lines through $p$. We introduce a natural stratification of  Hurwitz spaces according to the minimal degree of a plane curve such that a given meromorphic function can be represented in the above way and calculate the dimensions of these strata. We observe that they     are closely related to a family of Severi varieties studied earlier by J.~Harris, Z.~Ran and I.~Tyomkin. 

Place, publisher, year, edition, pages
2015. Vol. 58, no 3, 596-609 p.
Keyword [en]
Hurwitz spaces, meromorphic functions, Severi varieties
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-126347DOI: 10.4153/CMB-2015-015-xISI: 000359879900014OAI: oai:DiVA.org:su-126347DiVA: diva2:899230
Available from: 2016-02-01 Created: 2016-02-01 Last updated: 2017-09-03Bibliographically approved

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CiteExportLink to record
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  • apa
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