uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Sextic covers of genus two which are branched at three points
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Manuscript (Other academic)
URN: urn:nbn:se:uu:diva-95456OAI: oai:DiVA.org:uu-95456DiVA: diva2:169668
Available from: 2007-03-08 Created: 2007-03-08 Last updated: 2016-04-14Bibliographically approved
In thesis
1. Arithmetic of three-point covers
Open this publication in new window or tab >>Arithmetic of three-point covers
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Any cover of the Riemann sphere with rational branch points is known to be defined over the algebraic numbers. Hence the Galois group of the rationals acts on the category of such branched covers. Particulars about this action are still scarce, even in the simplest non-abelian case, the case with just three branch points.

The first paper in this thesis describes a new algorithm, which uses modular form techniques in order to compute the equations for a cover of the Riemann sphere which is hyperelliptic as a curve. Given such equations one may easily determine the Galois orbit to which the cover belongs. We compute and discuss all covers of degree 6 and genus 2, and complete the case of covers of degree 7 and genus 1 as well.

The second paper gives a proof of a formula for the number of three-point G-covers with a fixed special G-deformation datum (here G is a finite group which is strictly divisible by a prime number p). Since such a datum is an invariant for the action of the inertia group at p, this gives partial information about the action of this inertia group.

Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen, 2007. 30 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049
Algebra and geometry, Algebra och geometri
urn:nbn:se:uu:diva-7497 (URN)978-91-506-1916-4 (ISBN)
Public defence
2007-03-29, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Available from: 2007-03-08 Created: 2007-03-08 Last updated: 2009-08-25Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Strömbergsson, A
By organisation
Department of Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 153 hits
ReferencesLink to record
Permanent link

Direct link