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dc.contributor.authorHu, Xiaoyan
dc.date.accessioned2016-09-01T14:35:14Z
dc.date.available2016-09-01T14:35:14Z
dc.date.issued2014-08
dc.identifier.otherhu_xiaoyan_201408_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/hu_xiaoyan_201408_phd
dc.identifier.urihttp://hdl.handle.net/10724/35736
dc.description.abstractA Burniat surface $X$ is a particular surface of general type with $p_{g}=q=0$, $K_{X}^{2}=2,3,4,5mbox{ or }6$. Alexeev and Pardini constructed an explicit compactification of the moduli space of Burniat surfaces with $K_{X}^{2}=6$. In this thesis, we describe compactifications of moduli spaces of Burniat surfaces with $2leq K_{X}^{2}leq5$ obtained by adding KSBA surfaces, i.e. slc surfaces $X$ with ample canonical class $K_{X}$. We do it in two ways: by describing all one-parameter degenerations, and by using the theory of matroid tilings by matroid polytopes.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectBurniat surface
dc.subjectcompactification
dc.subjectmoduli space
dc.subjectcanonical model
dc.subjectstable pair
dc.subjectMMP
dc.subjectmatroid polytope
dc.subjectmatroid tiling
dc.subjectpolymake
dc.titleThe compactifications of moduli spaces of Burniat surfaces with $2leq k^{2}leq5$
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorValery Alexeev
dc.description.committeeValery Alexeev
dc.description.committeeRobert Varley
dc.description.committeeGordana Matic
dc.description.committeeAngela Gibney


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