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Towards Plane Hurwitz Numbers
Stockholm University, Faculty of Science, Department of Mathematics. University of Nairobi, Kenya. (Algebra and Geometry)
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The main objects of this thesis are branched coverings obtained as projection from a point in P^2. Our general goal is to understand how a given meromorphic function f: X -> P^1 can be induced from a composition X --> C -> P^1, where C is a plane curve in  P^2 which is birationally equivalent to the smooth curve X. In particular, we want to characterize meromorphic functions on plane curves which are obtained in such a way. For instance, we want to describe the relations on branching points of projections of plane projective curves of degree d and enumerate such functions. To this end, in a series of two papers, we show that any degree d meromorphic function on a smooth projective plane curve C of degree d > 4 is isomorphic to a linear projection from a point p belonging to P^2 \ C to P^1. Secondly, we introduce a planarity filtration of the small Hurwitz space using the minimal degree of a plane curve such that a given meromorphic function can be fit into a composition X --> C -> P^1. Finally, we also introduce the notion of plane Hurwitz numbers in this thesis.

Place, publisher, year, edition, pages
Stockholm: Stockholm University, Department of mathematics , 2014.
, Licentiate Thesis in Mathematics at Stockholm University
Keyword [en]
Algebraic curves, Hurwitz spaces
National Category
Algebra and Logic
Research subject
URN: urn:nbn:se:su:diva-103096ISBN: 978-91-7447-927-0OAI: diva2:715399
2014-06-05, 306, mathematics, department, Stockholms universitet, bldn 6, Stockholm, 10:00 (English)
Boris Shapiro
Available from: 2014-08-04 Created: 2014-05-05 Last updated: 2015-03-06Bibliographically approved

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