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dc.contributor.advisorHarris, Joeen_US
dc.contributor.authorPerry, Alexander Richarden_US
dc.date.accessioned2017-07-25T14:38:38Z
dc.date.created2016-05en_US
dc.date.issued2016-05-17en_US
dc.date.submitted2016en_US
dc.identifier.citationPerry, Alexander Richard. 2016. Derived categories and birational geometry of Gushel-Mukai varieties. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:33493330
dc.description.abstractWe study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, Hochschild cohomology, and the Grothendieck group. We study the K3 category associated to a Gushel-Mukai fourfold in more detail. Namely, we show that this category is equivalent to the derived category of a K3 surface for a certain codimension 1 family of rational fourfolds, and to the K3 category of a birational cubic fourfold for a certain codimension 3 family. The first of these results verifies a special case of a duality conjecture which we formulate. We discuss our results in the context of the rationality problem for Gushel-Mukai varieties, which was one of the main motivations for this work.en_US
dc.description.sponsorshipMathematicsen_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoenen_US
dash.licenseLAAen_US
dc.subjectMathematicsen_US
dc.titleDerived categories and birational geometry of Gushel-Mukai varietiesen_US
dc.typeThesis or Dissertationen_US
dash.depositing.authorPerry, Alexander Richarden_US
dc.date.available2017-07-25T14:38:38Z
thesis.degree.date2016en_US
thesis.degree.grantorGraduate School of Arts & Sciencesen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
dc.contributor.committeeMemberMazur, Barryen_US
dc.contributor.committeeMemberMaulik, Daveshen_US
dc.type.materialtexten_US
thesis.degree.departmentMathematicsen_US
dash.identifier.vireohttp://etds.lib.harvard.edu/gsas/admin/view/1079en_US
dc.description.keywordsalgebraic geometry; derived categories; birational geometryen_US
dash.author.emailarptron@gmail.comen_US
dash.contributor.affiliatedPerry, Alexander


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