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Donaldson-Thomas theory of quantum Fermat quintic threefolds Liu, Yu-Hsiang
Abstract
In this thesis, we study non-commutative projective schemes whose associated graded algebras are finite over their centers. We construct symmetric obstruction theories for their moduli spaces of stable sheaves in the Calabi–Yau-3 case. This allows us to define Donaldson–Thomas (DT) type deformation invariants. As an application, we study the quantum Fermat quintic threefold which is the quintic threefold in a quantum projective space. We give an explicit description of its local models in terms of quivers with potential. We then give a full computation of its degree zero DT invariants.
Item Metadata
| Title |
Donaldson-Thomas theory of quantum Fermat quintic threefolds
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
2020
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| Description |
In this thesis, we study non-commutative projective schemes whose associated graded algebras are finite over their centers. We construct symmetric obstruction theories for their moduli spaces of stable sheaves in the Calabi–Yau-3 case. This allows us to define Donaldson–Thomas (DT) type deformation invariants.
As an application, we study the quantum Fermat quintic threefold which is the quintic threefold in a quantum projective space. We give an explicit description of its local models in terms of quivers with potential. We then give a full computation of its degree zero DT invariants.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2020-07-21
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0392485
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2020-11
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International