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Dmitri Skjorshammer

Picture of Dmitri Skjorshammer.


Tops in Higher Dimensions

Ursula Whitcher
Second Reader(s)
Dagan Karp


Reflexive polytopes can be used to construct families of Calabi-Yau varieties as hypersurfaces in toric varieties. Reflexive polytopes have been classified for $n \leq 4$ by constructing maximal objects that contain all reflexive polytopes as subsets. Given computational constraints, classification becomes intractable for $n = 5$. An alternate approach is to make use of tops, which are generalizations of the notion of half of a reflexive polytope. In this thesis, we investigate classification algorithms for tops and construct a class of four-dimensional tops which can be completed to reflexive polytopes. We then outline how this all relates to fiber bundles on toric varieties.


Classification of Tops in Five Dimensions

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