Show simple item record

AuthorHanselman, Jeroendc.contributor.author
Date of accession2020-10-14T13:38:29Zdc.date.accessioned
Available in OPARU since2020-10-14T13:38:29Zdc.date.available
Year of creation2020dc.date.created
Date of first publication2020-10-14dc.date.issued
AbstractGiven two curves, X of genus g1 and Y of genus g2, one can consider the product P = Jac(X) x Jac(Y) of the Jacobians of these curves and try to find a curve of genus g_1+g_2, whose Jacobian is isogenous to P. Because of the isogeny, the constructed curve will inherit a number of properties from the two lower genus curves. For example, the endomorphism algebra of the Jacobian of the new curve will be isomorphic to the product of the endomorphism algebras of the two lower genus Jacobians. In this thesis we study two different algorithms to calculate (2,2)-gluings of a genus 2 curve Y and a genus 1 curve X along their 2-torsion. By this we mean that we construct a genus 3 curve whose Jacobian is the quotient of Jac(X)xJac(Y) by a 2-torsion subgroup in such a way that the polarizations on both sides are in some way compatible. One algorithm is purely analytical and works by calculating period matrices. Another algorithm is purely algebraic and uses a construction involving Kummer surfaces.dc.description.abstract
Languageen_USdc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHCurves (Algebraic)dc.subject.lcsh
LCSHArithmetical algebraic geometrydc.subject.lcsh
LCSHJacobiansdc.subject.lcsh
TitleGluing curves of genus 2 and genus 1 along their 2-torsiondc.title
Resource typeDissertationdc.type
Date of acceptance2020-07-30dcterms.dateAccepted
RefereeSijsling, Jeroendc.contributor.referee
RefereeBouw, Irenedc.contributor.referee
DOIhttp://dx.doi.org/10.18725/OPARU-33350dc.identifier.doi
PPN1735708062dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-oparu-33412-0dc.identifier.urn
GNDAlgebraische Geometriedc.subject.gnd
GNDArithmetische Geometriedc.subject.gnd
GNDJacobi-Mannigfaltigkeitdc.subject.gnd
GNDAlgebraische Kurvedc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
InstitutionInstitut für Reine Mathematikuulm.affiliationSpecific
Grantor of degreeFakultät für Mathematik und Wirtschaftswissenschaftenuulm.thesisGrantor
DCMI TypeTextuulm.typeDCMI
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record