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Title: Calabi-Yau categories and quivers with superpotential
Author: Lam, Yan Ting
ISNI:       0000 0004 5353 2772
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2014
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This thesis studies derived equivalences between total spaces of vector bundles and dg-quivers. A dg-quiver is a graded quiver whose path algebra is a dg-algebra. A quiver with superpotential is a dg-quiver whose differential is determined by a "function" Φ. It is known that the bounded derived category of representations of quivers with superpotential with finite dimensional cohomology is a Calabi- Yau triangulated category. Hence quivers with superpotential can be viewed as noncommutative Calabi- Yau manifolds. One might then ask if there are derived equivalences between Calabi-Yau manifolds and quivers with superpotential. In this thesis, we answer this question and, generalizing Bridgeland [15], give a recipe on how to construct such derived equivalences.
Supervisor: Joyce, Dominic Sponsor: Croucher Foundation
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Algebraic geometry ; Geometry ; Representation Theory ; Calabi-Yau Categories ; Quivers with Superpotential ; Derived Equivalences ; Tilting ; McKay Quivers ; Koszul Functor