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dc.contributor.authorRusinko, Jo
dc.date.accessioned2014-03-04T02:47:36Z
dc.date.available2014-03-04T02:47:36Z
dc.date.issued2007-08
dc.identifier.otherrusinko_joseph_p_200708_phd
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/rusinko_joseph_p_200708_phd
dc.identifier.urihttp://hdl.handle.net/10724/24268
dc.description.abstractBatyrev (et. al.) constructed a family of Calabi-Yau varieties using small toric degen- erations of the full flag variety G/B. They conjecture this family to be mirror to generic anticanonical hypersurfaces in G/B. Recently Alexeev and Brion, as a part of their work on toric degenerations of spherical varieties, have constructed many degenerations of G/B. For any such degeneration we construct a family of varieties, which we prove coincides with Batyrev’s in the small case. We prove that any two such families are birational, thus proving that mirror families are independent of the choice of degeneration. The birational maps involved are closely related to Berenstein and Zelevinsky’s geometric lifting of tropical maps to maps between totally positive varieties.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjectCalabi-Yau
dc.subjectMirror Symmetry
dc.subjectToric Degenerations
dc.titleEquivalence of mirror families constructed by toric degenerations of flag varieties
dc.typeDissertation
dc.description.degreePhD
dc.description.departmentMathematics
dc.description.majorMathematics
dc.description.advisorValery Alexeev
dc.description.committeeValery Alexeev
dc.description.committeeMiljenko Zabcic
dc.description.committeeRobert Varley
dc.description.committeeMitch Rothstein
dc.description.committeeWilliam Graham


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