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Towards Plane Hurwitz NumbersPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Stockholm University, Department of mathematics , 2014.
##### Series

Licentiate Thesis in Mathematics at Stockholm University
##### Keyword [en]

Algebraic curves, Hurwitz spaces
##### National Category

Algebra and Logic
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-103096ISBN: 978-91-7447-927-0 (print)OAI: oai:DiVA.org:su-103096DiVA, id: diva2:715399
##### Presentation

2014-06-05, 306, mathematics, department, Stockholms universitet, bldn 6, Stockholm, 10:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Projects

Boris Shapiro
Available from: 2014-08-04 Created: 2014-05-05 Last updated: 2015-03-06Bibliographically approved

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.

isbn
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