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A Note on Planarity Stratification of Hurwitz Spaces
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 2
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 CP2 and a projection of the image curve from an appropriate point p is an element of CP2 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 Seven 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
Identifiers
URN: urn:nbn:se:su:diva-120890DOI: 10.4153/CMB-2015-015-xISI: 000359879900014OAI: oai:DiVA.org:su-120890DiVA: diva2:945022
Available from: 2016-06-30 Created: 2015-09-18 Last updated: 2016-06-30Bibliographically approved

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Shapiro, Boris
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