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dc.contributor.authorBoulter, Eric
dc.date.accessioned2023-04-20 12:42:35 (GMT)
dc.date.available2023-04-20 12:42:35 (GMT)
dc.description.abstractThis thesis studies two problems relating to moduli spaces of vector bundles on non-Kähler elliptic surfaces. The first project involves the holomorphic symplectic structure on smooth and compact moduli spaces of sheaves on Kodaira surfaces. We show that these moduli spaces are neither Kähler nor simply connected. Comparing to other known examples of compact holomorphic symplectic manifolds, this shows that if the moduli spaces are deformation equivalent to a known example, then they are Douady spaces of points on a Kodaira surface. The second problem deals with the interplay between singularities of moduli spaces of rank-2 vector bundles and existence of stable Vafa--Witten bundles on non-Kähler elliptic surfaces. By constructing a Vafa--Witten bundle in each filtrable Chern class of the elliptic surface when the base has genus g≥2, we show that such a moduli space is smooth as a ringed space if and only if every bundle in the moduli space is irreducible.en
dc.publisherUniversity of Waterlooen
dc.subjectholomorphic vector bundlesen
dc.subjectholomorphic symplectic manifoldsen
dc.subjectelliptic surfacesen
dc.subjectmoduli spacesen
dc.subjectHiggs bundles and generalisationsen
dc.subjectnon-Kähler manifoldsen
dc.titleVector Bundles on Non-Kähler Elliptic Surfacesen
dc.typeDoctoral Thesisen
uws-etd.degree.departmentPure Mathematicsen
uws-etd.degree.disciplinePure Mathematicsen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorMoraru, Ruxandra
uws.contributor.affiliation1Faculty of Mathematicsen

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