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dc.contributor.authorElek, Balazs
dc.identifier.otherbibid: 10489561
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.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.titleToric surfaces with Kazhdan-Lusztig atlases
dc.typedissertation or thesis University of Philosophy D., Mathematics
dc.contributor.chairKnutson, Allen
dc.contributor.committeeMemberSjamaar, Reyer
dc.contributor.committeeMemberBarbasch, Dan Mihai

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