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dc.contributor.authorMolnar, Alexander
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date2015-09-10 15:28:19.743en
dc.date.accessioned2015-09-10T21:43:46Z
dc.date.available2015-09-10T21:43:46Z
dc.date.issued2015-09-10
dc.identifier.urihttp://hdl.handle.net/1974/13588
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2015-09-10 15:28:19.743en
dc.description.abstractThis thesis is centered around particular Calabi-Yau threefolds. Borcea \cite{Borcea} and Voisin \cite{Voisin} construct Calabi-Yau threefolds using elliptic curves and K3 surfaces with non-symplectic involutions. This family has an incredible property, that a general member has a mirror pair within this family. We start by investigating if this construction works only for Calabi-Yau threefolds with non-symplectic involutions or with non-symplectic automorphisms of higher order as well. Thereafter, we generalize this construction to Calabi-Yau fourfolds. After this, we focus on the underlying construction that lead Borcea to the families above, using a product of three elliptic curves with non-symplectic involutions. These threefolds do not come in families, so we cannot ask about mirror symmetry, but if we have models defined over $\Qbb$, we may ask arithmetic questions. Many arithmetic properties of the Calabi-Yau threefolds can be studied via the underlying elliptic curves. In particular, we are able to show (re-establish in the rigid case) that the Calabi-Yau threefolds are all modular by computing their $L$-functions. Then, guided by a conjecture of Yui, we investigate their (Griffiths) intermediate Jacobians and a relationship between their respective $L$-functions.en_US
dc.language.isoengen_US
dc.relation.ispartofseriesCanadian thesesen
dc.rightsQueen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canadaen
dc.rightsProQuest PhD and Master's Theses International Dissemination Agreementen
dc.rightsIntellectual Property Guidelines at Queen's Universityen
dc.rightsCopying and Preserving Your Thesisen
dc.rightsCreative Commons - Attribution - CC BYen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectNumber theoryen_US
dc.subjectModularityen_US
dc.subjectCalabi-Yau varietiesen_US
dc.subjectIntermediate Jacobianen_US
dc.subjectArithmetic geometryen_US
dc.titleArithmetic and Intermediate Jacobians of Calabi-Yau threefoldsen_US
dc.typethesisen_US
dc.description.degreePh.Den
dc.contributor.supervisorYui, Norikoen
dc.contributor.departmentMathematics and Statisticsen


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