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dc.contributor.authorElek, Balazs
dc.date.accessioned2018-10-23T13:23:27Z
dc.date.available2018-10-23T13:23:27Z
dc.date.issued2018-05-30
dc.identifier.otherElek_cornellgrad_0058F_10829
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:10829
dc.identifier.otherbibid: 10489561
dc.identifier.urihttps://hdl.handle.net/1813/59476
dc.description.abstractA Kazhdan-Lusztig atlas, introduced by He, Knutson and Lu, on a stratified variety (V,Y) is a way of modeling the stratification Y of V locally using the stratification of Kazhdan-Lusztig varieties. We are interested in classifying smooth toric surfaces with Kazhdan-Lusztig atlases. This involves finding a degeneration of V to a union of Richardson varieties in the flag variety H/B_H of some Kac-Moody group H. We determine which toric surfaces have a chance at having a Kazhdan-Lusztig atlas by looking at their moment polytopes, then describe a way to find a suitable group H. More precisely, we find that (up to equivalence) there are 19 or 20 broken toric surfaces admitting simply-laced atlases, and that there are at most 7543 broken toric surfaces where H is any Kac-Moody group.
dc.language.isoen_US
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subjectMathematics
dc.titleToric surfaces with Kazhdan-Lusztig atlases
dc.typedissertation or thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Mathematics
dc.contributor.chairKnutson, Allen
dc.contributor.committeeMemberSjamaar, Reyer
dc.contributor.committeeMemberBarbasch, Dan Mihai
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/X4NZ85WK


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