On the Classification of Enriques Surfaces

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dc.contributor.advisorBaraglia, David
dc.contributor.advisorBuchdahl, Nicholas
dc.contributor.authorTchorbadjiev, Radee Stefanov
dc.contributor.schoolSchool of Computer and Mathematical Sciences
dc.date.issued2025
dc.description.abstractIn 1958, André Weil formulated a number of famous conjectures concerning the structure of K3 surfaces: all such surfaces are deformation equivalent; they all admit K¨ahler structures; every point of the period domain arises as the period point of a K3 surface; and the biholomorphism class of a K3 surface is determined by its period point. By appealing to the fact that every Enriques surface is double-covered by a K3 surface, one can in a natural way extend the considerations of the period map of K3 surfaces to the case of Enriques surfaces. In this case, one obtains analogous results for Enriques surfaces, and it is with their proof that the present work is concerned. By making use primarily of the classification results of K3 surfaces, as well as their moduli space of Einstein metrics, we provide short, independent proofs of the results concerning Enriques surfaces which taken together fully classify this important class of compact complex surface of Kodaira dimension 0. We conclude by extending the above considerations to the case of quotients of Enriques surfaces by free anti-holomorphic involutions where we prove that these resulting compact Einstein four-manifolds are diffeomorphic, and in fact of the same deformation type.
dc.description.dissertationThesis (MPhil) -- University of Adelaide, School of Computer and Mathematical Sciences, 2025en
dc.identifier.urihttps://hdl.handle.net/2440/146223
dc.language.isoen
dc.provenanceThis electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legalsen
dc.subjectDifferential Geometry
dc.subjectComplex Geometry
dc.subjectAlgebraic Geometry
dc.titleOn the Classification of Enriques Surfaces
dc.typeThesisen

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